1) The complement of an event A is given by A' . which of the following are true ?
A) P(A) + P(A')= 1
B) P(A) + P(A')= 0
C) P(A and A')=0
D) Both A and C above.
2) If one event is unaffected by the outcome of another event, the two events are said to be
A) dependent B) independent.
C) mutually exclusive D) all
3) two events are mutually exclusive if
A) their probability are less than 1
B) their probabilities sum to 1
C) they cannot occur at the same time.
D) they contain every possible outcome of an experiment
4) if P(A or B)= P(B)
A) A and B must be mutually exclusive
B) A and B must be independent
C) P(A)= P(B)
D) occurrence of A implies occurrence of B.
5) For any two events A and B implies which of the following is it true ?
A) P(A or B)=P(A)+ P(B)
B) P(A and B)=P(A) x P(B)
C) P(A or B)=P(A)+ P(B) - P(A) x P(B)
D) P(A or B)=P(A)+ P(B) - P(A and B).
6) A and B are two non exclusive events such that P(A) + P(B) - P(A and B) = P(A) then
A) P(B/A)= 1 B) P(A/B)=1.
C) P(A/B')= 0 where B' is complement of B
D) P(B/A')=1 where A' is complement of A
7) There are four letters to be put into four addressed envelopes. If the letters are placed at random into the envelopes, the probability that all the letters go into correct envelopes is:
A) 1/24. B) 2/47 C) 1/16 D) 2/19
8) If the occurrence of A is unaffected by the occurance of B, then A and B are
A) dependent B) independant.
C) mutually exclusive
D) both A and C
9) A fund manager finds that the price of Raliance has 50% probability of crossing ₹200 mark, 10% probability of crossing ₹225 mark and 30% probability of declining to a level of less than ₹175 mark in the next two months. This is an example of
A) marginal probability
B) subjective probability.
C) conditional probability
D) joint Probability
10) P(A/B)= P(A), then A and B are
A) dependent B) independent.
C) conditional
D) mutually exclusive
11) An probability is
A) an event
B) a favourable outcome
C) A chance.
D) an outcome of an experiment
12) If P(A')= P(B)= 1 - P(A) then
A) events A and B have the same probability
B) P(A and A')=1
C) events A and B are collectively exhaustive.
D) P(A' and B')= 1
13) In Venn diagram, if events A and B do not overlap on each other, then events A and B are
A) mutually exclusive.
B) not mutually exclusive
C) independent D) dependent
14) If P(A or B)= P(A)+ P(B) then A and B are
A) independent B) dependent
C) conditional
D) mutually exclusive.
15) If marginal probability of A is x and marginal probability of B is y, then the marginal probability of A and B will be
A) x+y B) x - y.
C) (1-x)(1-y) D) x+ y - xy
16) If [1- P(A)]= P(B) then events A and B are
A) independent
B) not mutually exclusive
C) collectively exhaustive.
D) dependent
17) which of the following is true for mutually exclusive events ?
A) P(A or B or C)= P(A)+P(B)+P(C).
B) P(A and B and C)= P(A)+P(B)+P(C)
C) P(A or B or C)= P(A)+P(B)+P(C) - P(AB) - P(BC) - P(CA)
D) P(A and B and C)= P(A)+P(B)+P(C) - P(AB) - P(BC) - P(CA)
18) In a Venn diagram, if events A and B do not overlap with each other whereas A and B both overlap with event C, then P(A or B or C) will be equal to
A) P(A) + P(B) + P(C)
B) P(A)+P(B)+P(C) - P(A and B) - P(A and C)
C) P(A) + P(B) + P (C) - P(B andC) - P(C and A).
D) P(A)+P(B)+P(C) - P(A and B) - P(C and B)
19) The probability of an event 'A' occurring is p. If the experiment is conducted n times, the probability of 'A' occurring every time will be
A) 1 B) close to 1
C) close to zero D) "p"
20) Baye's Theorem allows us to revise.
A) prior probabilities
B) posterior probabilities.
C) unique probabilities
D) subjective probability
21) an investment expert states that the returns on stock markets in the next year will be 26% whereas Infostock will fetch above 35% returns. this is an example of
A) classical probability
B) probability distribution of returns
C) subjective probability.
D) relative events
22) which of the following is not correct ?
A)P(A/B)= P(A and B)/P(B)
B) P(A and B)= P(A).P(B)A)
C) P(A and B)= PP(B/A). P(A).
D) P(A or B)= P(B). P(A/B)
23) The possible outcomes favourable for an event and the total number of outcomes are known without performing the experiment in case of
A) classical probability.
B) marginal probability
C) relative probability
D) subjective probability
24) the knowledge of which of the following is likely to help most in decision making ?
A) apriori probabilities
B) posterior probabilities.
C) conditional probabilities
D) classical probabilities
25) in which of the following cases the outcomes favourable for an event and the total number of outcomes must be known without performing the experiment ?
A) classical probability.
B) marginal probability
C) relative probability
D) subjective probability
26) Ram picked prime number from the set of first 20 natural numbers. what is the probability that it is 7 ?
A) 1/7 B) 1/19 C) 1/8. D) none
27) Baye's theorem is a formula for
A) unconditional Probability under statistical Independence.
B) unconditional Probability under statistical dependence
C) conditional Probability under statistical independence
D) conditional Probability under statistical dependence.
28) An event A having a zero probability can be shown in the Vain diagram as
A) a point . B) a circle
C) a rectangle D) an ellipse
29) If P(A')= P(B) then A and B are
A) independent
B) mutually exclusive
C) collectively exhaustive
D) both B and C.
30) in which of the following cases does the probability estimate of the occurrence of a particular event differ from one decision-maker to another ?
A) classical probability
B) marginal probability
C) subjective probability.
D) mutually exclusive events
31) If two events A and B are mutually exhaustive and collectively exclusive and collectively exhaustive then
A) P(A B)=0 and P(A) + P(B) =1.
B) P(A B)= 1 and P(A) + P(B) =1
C) P(A B)=1 and P(A) + P(B) =0
D) P(A B)>0 and P(A) + P(B) =1
32) If two events A and B are not mutually exclusive then the probability that neither A nor B occurs is equals to
A) 1 - P(A B) B) P(A B) - 1
C) 1 - [P(A) + P(B) - P(AB).
D) P(A) + P(B) - P(AB) - 1
33) Which of the following statement is true ?
A) marginal Probability and conditional probability are same
B) joint probability, marginal Probability, and conditional probability are all same
C) aprior Probability and posterior probability are same
D) there is no point in calculating the joint probability of mutually exclusive events.
34) the probability that numbers selected from {1, 2,3,4 ....100} is a perfect cube is
A) 1/10 B)1/25. C)3/200 D)5/100
35) Two events A and B are such that their joint probability is equal to the product of their marginal probabilities. which of the following best describes events A and B ?
A) A and B are dependent events
B) A and B are independent events.
C) A and B are mutually exclusive events
D) A and B are collectively exhaustive events
36) If two events A and B are independent then, the conditional probability of event A given that event B has occurred, is equals to
A) joint probability of events A and B
B) condition probability of the event B given event A
C) marginal probability of event B
D) marginal probability of event A.
37) which of the following are the conditions for applying the Baye's theorem for computing posterior probabilities of certain events ?
A) the event must be non mutually exclusive
B) the event must be mutually exclusive
C) The events must not be collectively exhaustive
D) the events must be collectively exhaustive.
38) which of the following statements is most appropriate if certain events are mutually exclusive and collectively exhaustive ?
A) each of the event has zero probability
B) some of the event will definitely have a zero probability
C) the sum of the probabilities of the events will be equals to 1.
D) the sum of the probabilities of the events will be less than 1
39) which of the following is true with regard to classical approach to probability?
A) assume that the outcomes are not equally likely
B) the probability of an event is determined after performing the experiment large number of times
C) the probability of an event is determined before performing the experiment.
D) it assumes that all possible outcomes of the experiment are not known
40) the probability of the occurrence of an event is expressed as a number which lies between
A) 0 and 1. B) 1 and 2
C) -1 and 0 D) - 2 and -1
41) events A and B are dependent. The joint probability of the events A and B is
A) equals to the product of the events A and B
B) not equal to the product of the marginal probabilities of the events A and B.
C) equal to the sum of the marginal Probabilities of the events A and B
D) equal to the difference between the marginal Probabilities of the events A and B
** two coins are tossed simultaneously. find the probability of getting
42) all heads
A) 1/4. B) 1/2 C) 3/4 D) none
43) all tails
A) 1/4. B) 1/2 C) 3/4 D) none
44) no heads
A) 1/4. B) 1/2 C) 3/4 D) none
45) No Tales
A) 1/4. B) 1/2 C) 3/4 D) none
46) at least one head
A) 1/4 B) 1/2 C) 3/4. D) none
47) at least one tail
A) 1/4 B) 1/2 C) 3/4. D) none
48) all not heads
A) 1/4 B) 1/2. C) 3/4 D) none
49) almost one head
A) 1/4 B) 1/2 C) 3/4. D) none
50) heads will come in First row
A) 1/4 B) 1/2. C) 3/4 D) none
51) Heads and tails will occur alternatively.
A) 1/4 B) 1/2. C) 3/4 D) none
** three coins are tossed simultaneously. find the probability of getting:
52) all heads
A) 1/8. B) 6/8 C) 7/8 D) 4/8
53) Alk tails
A) 1/8. B) 6/8 C) 7/8 D) 4/8
54) No head
A) 1/8. B) 6/8 C) 7/8 D) 4/8
55) no tail
A) 1/8. B) 6/8 C) 7/8 D) 4/8
56) at least one head
A) 1/8 B) 6/8 C) 7/8. D) 4/8
57) at least one tail
A) 1/8 B) 6/8 C) 7/8. D) 4/8
58) all not heads
A) 1/8 B) 6/8 C) 7/8. D) 4/8
59) at least two heads
A) 1/8 B) 6/8 C) 7/8 D) 4/8.
60) at most two tails
A) 1/8 B) 6/8 C) 7/8. D) 4/8
61) at most one head
A) 2/8. B) 6/8 C) 1/8 D) 4/8
62) two or more tails
A) 1/8 B) 6/8 C) 7/8 D) 4/8.
63) more than two tails
A) 1/8 B) 6/8 C) 7/8. D) 4/8
64) less than one head
A) 1/8 B) 6/8 C) 7/8. D) 4/8
65) heads and Tails
A) 1/8 B) 6/8. C) 7/8 D) 4/8
66) heads are two extremes
A) 1/8. B) 6/8 C) 7/8 D) 4/8
67)heads will come in the 1st row
A) 1/8 B) 6/8 C) 7/8 D) 4/8.
68) heads will exceed the number of tails in a particular throw
A) 2/8 B) 6/8 C) 1/8 D) 4/8.
***a card is drawn from a well shuffled pack of 52 cards. find the probability that--
69) it is red
A) 1/4 B) 1/2. C)1/5 D) 33/56
70) it is an Ace
A) 2/13 B) 3/13 C) 1/13. D) 4/13
71) it is a spade
A) 2/8. B) 6/8 C) 1/8 D) 4/8
72) it is either a king or an Ace
A) 2/13. B) 3/13 C) 1/13 D) 4/13
73) It is either King or a Knave
A) 2/13. B) 11/13 C) 10/13 D) 4/13
74) it is neither a king nor a Knave.
A) 2/13 B) 11/13. C) 10/13 D) 4/13
75) It is neither a heart nor a Diamond.
A) 0.45 B) 0.50. C) 0.75 D) 0.80
76) it is neither an Ace nor a king, nor a Queen nor a Knave
A) 12/13 B) 11/13 C) 10/13 D) 9/13.
77) A spade or an ace not of spade
A) 2/13 B) 4/13. C) 1/13 D) 7/13
** A bag contains 3 Green 8 white balls. If one ball is drawn at random, find the chance that:
78) it is Green
A) 1/11 B) 2/11 C) 3/11 D) 4/11
79) it is white
A) 2/11 B) 4/11 C) 6/11 D) 8/11
** A bag contains 3 green and 8 white balls.
If two balls are drawn, find the chance that
80) both are green.
A) 5/55 B) 2/55 C) 3/55 D) 6/55
81) both are white
A) 25/55 B) 28/55 C) 23/55 D)26/55
82) one green and white
A) 25/55 B) 42/55 C) 24/55 D) 6/55
** a bag contains 3 Green and 8 white balls.
If three balls are drawn, find the chance that :
83) All are green
A) 5/165 B)1/165C)3/165D)6/165
84) All are white
A) 56/165 B)61/165
C)63/165 D)66/165
85) Two green and one white
A) 25/165 B)21/165
C) 24/165 D) 26/165
86) one green and two white
A) 85/165 B) 81/165
C) 23/165 D) 84/165
** from a bag containing 7 white and 5 red balls , 4 balls are drawn at random. what is the chance that :
87) all are white
A) 35/490 B) 35/495
C) 43/495. D) none
88) all our red
A) 5/495 B) 1/495
C) 3/495. D) noneto
89) two White and 2 red
A) 225/495 B) 210/495
C) 259/495. D) 265/395
90) 3 white in one red
A) 165/495 B) 185/495
C) 175/495. D) 195/495
91) 3 red and one white
A) 75/495 B) 81/495
C) 73/495. D) 70/495
92) there are 17 balls numbered 1 to 17 in a bag, if a person selects one ball random, find the probability that the number printed on the ball will be an even number greater than 9.
A) 5/17 B) 4/17 C) 3/17 D) 2/17
** A bag contains seven 1 rupee coins, seven 50p. coins and 25p. Coins. Find the probability of drawing:
93) 1 one rupee coin.
A) 3/18 B) 2/18 C) 1/18 D) 4/18
94) Three 1 rupee coins
A) 53/816 B) 35/816
C) 81/816 D) 41/816
95) Three coins, one of each
A) 153/816 B) 135/816
C) 196/816 D) none
96) Find the chance of not throwing an ace, two or three in a single cast with a die.
A) 0.33 B)0.75 C)0.50 D) 0.85
** 5 men in a company of 20 are graduates. If 3 men are picked out of the 20 at random, find the probability that;
97) they are all a graduates.
A) 1/141 B) 1/114
C) 1/411 D) none
98) there is no graduate
A) 545/1140. B) 455/1140
C) 554/1140 D) none
99) there is at least one graduate
A) 645/1140. B) 655/1140
C) 685/1140 D) none
** two cards are drawn at random from a well shuffled pack of 52 cards. Find the probability that :
100) both are spades
A) 87/1326 B) 77/1236
C) 78/1326. D) none
101) both are King
A) 1/221 B) 4/1326
C) 2/1326. D) none
102) one spade and other is heart
A) 182/1326. B) 177/1326
C) 169/1326. D) 179/1326
** A sub committee of 6 members is to be formed out of a group consisting of 7 men and 4 ladies. Calculate the probability that the sub committee will consist of;
103) exactly two ladies
A) 210/460. B) 105/231
C) 108/231. D) 110/231
104) At least two ladies
A) 278/462 B) 378/462
C) 287/462 D) none
** two dice are rolled. find the probability that
105) sum of the face is 7
A) 1/4 B) 1/8 C) 1/6 D) none
106) Sum is 11
A) 1/14 B) 5/36 C) 1/18 D) none
107) it is either 7 or 11
A) 3/9 B)5/9 C) 2/9 D) none
108) it is neither 7 nor 11
A) 5/9 B) 3/9 C) 7/9 D) none
109) sum is an odd number more than 3.
A) 2/9 B) 4/9 C) 6/9 D) none
110) sum is a multiple of 3.
A) 1/9 B) 2/9 C) 3/9 D) none
111) sum is a multiple of 4.
A) 1/6 B) 1/3 C) 1/4 D) 1/36
112) sum is a multiple of 3 and 4
A) 2/36 B) 3/36 C) 4/36 D) 1/36
113) sum is a multiple of 3 or 4.
A) 5/9 B) 3/9 C) 7/9 D) none
114) sum at least 8.
A) 4/12 B) 5/12 C) 6/12 D) none
115) sum is at most 7
A) 4/12 B) 5/12 C) 7/12 D) none
116) the product of the face is 12
A) 3/9 B) 2/9 C) 1/9 D) none
117) sum of the faces is more than 12
A) 4/12 B) 2/12 C) 1/12 D) none
*** two letters are drawn from the word HOME. Find the chance that:
118) letters are vowels
A) 1/6 B) 2/6 C) 3/6 D) 4/6
119) at least one is a vowel
A) 1/6 B) 2/6 C) 3/6 D) 5/6
120) one of the letters choosen is H
A) 1/6 B) 2/4 C) 3/4 D) 4/6
121) Out of the five players of which two are members of the certain club, 3 are to be selected to represent the country at an international tournament. find the probability that less than two of those selected to represent are members of the club.
A) 0.75 B)0.60 C) 0.80 D) 0.70
122) the weekly wages of 6 workers in a factory are ₹62, 90, 78, 85, 79, ,68. two of the labourers are to be selected at random to serve as representatives. what is the probability that atleast one will have a wage lower than the average ?
A) 0.40 B) 0.50 C) 0.60 D) none
123) there are four hotels in a town and 3 person entred the town. find the probability that they check into different hotels.
A) 0.475 B) 0.325
C) 0.375 D) none
*** three dice are rolled.
find the probability that:
124) The faces will show three 5's
A) 2/216. B) 3/216
C) 1/216. D) none
125) The faces will show 2,4,6
A)2/72 B)1/33 C) 3/96 D) none
126) the faces will show 5,66
A) 2/72 B) 1/72 C) 3/72 D) none
127) 5 numbers are selected at random from the set of first 50 natural numbers and arranged in a following order a,b,c,d,e. find the probability that c= 30
A) (²⁹C₂ . ¹C₀ . ²⁰C₂)/ ⁵⁰C₅
B) (²⁹C₂. ¹C₁.²⁰C₂)/ ⁵⁰C₅
C) (²⁹C₂ .²⁹C₃ )/⁵⁰C₃
D) none
128) 20 dates and named at random. find the probability that there are exactly 5 sundays.
A) ²⁰C₅/7¹⁵ B) ²⁰C₅ /7²⁰
C) ²⁰C₅.6 ²⁰/7²⁰ D) ²⁰C₅. 6¹⁵/7²⁰
129) A League match in football a
end WIN, LOSS or DRAW, Being a supporter of a club, find the probability that exactly 18 correct results can be predicted if 22 matches are played in all
A) ²⁰C₁₈. 2⁴/22³ B) ²²C₁₈.2⁴/22 ³
C) ²⁰C₁₈. 2⁴/3²² D) ²²C₁₈.2⁴/3²²
130)10 balls are distributed in 3 boxes. Find the probability that a particular box will contain exactly 3 balls
A) ¹⁰C₃.2⁷)10³ B) ¹⁰C₃.2⁷/3¹⁰
C) ³⁰C₃.2⁷/3¹⁰. D) NONE
131) If 'n' Biscuits are distributed at random to 'N' person, find the probability that the particular person will get exactly 't' no. of Biscuits.
A) ᴺCᵣ .(n-1)ᴺ⁻ʳ /nᴺ
B) ⁿCᵣ(N-1)ⁿ⁻ʳ/Nⁿ
C) ᴺCᵣ(n-1)ᴺ⁻ʳ /Nⁿ
D) None
132) If 10 biscuits are distributed at random to 3 persons, then find the probability that a particular person will get exactly 2 biscuits.
A) ¹⁰C₃ .2⁷/10³
B) ¹⁰ C₃2⁷/3¹⁰
C) ³⁰C₃ .2⁷/3¹⁰ D) none
** A nine digit number is to be formed with the digit 1,2,3...,9. Find the probability that
133) the number should begin with 5.
A) 3/9 B) 2/9 C) 4/9 D) 1/9
134) it should end with 9.
A) 1/9 B) 2/9 C) 3/9 D) 4/9
135) it should be begin with 5 and end with 9.
A) 2/72 B)12/72 C) 1/72 D) 11/72
136) It should begin with 5 but not end with 9.
A) 7/72 B)12/72 C) 1/72 D) 11/72
137) 5 and 9 are at the two extremes.
A) 1/72 B) 2/72 C) 3/72 D) 4/72
138) the digits 5 should always be in odd places
A)35/72 B)45/72 C) 40/72 D) none
139) the digit 5 should occur at even places.
A) 1/9 B) 2/9 C) 3/9 D) 4/9
140) the digits 5 and 9 together
A) 1/9 B) 2/9 C) 3/9 D) 4/9
141) the digits 5 and 9 are together in the given order.
A) 1/9 B) 2/9 C) 3/9 D) 4/9
142) The digit 5 will never come together.
A) 1/9 B) 2/9 C) 3/9 D) 7/9
143) the digits 1, 2, 3 are together.
A) 1/12 B) 2/12 C) 3/12 D) none
144) the digits 1,2, 3 are together in a given order.
A) 41/72 B) 1/72 C) 11/72 D)none
** In a family of 3 children there is at least one girl. find the probability that :
145) there are all girl.
A) 1/8 B) 2/7 C) 2/8 D) 1/7
146) there exactly two boys.
A) 1/8 B) 3/7 C) 2/8 D) 1/7
147) there are at least two girls.
A) 4/7 B) 2/7 C) 2/8 D) 1/7
148) there is exactly one boy.
A) 1/8 B) 2/7 C) 3/7 D) 1/7
149) there is at most one boy.
A) 1/8 B) 4/7 C) 2/8 D) 1/7
150) all are not girls.
A) 6/7 B) 3/7 C) 6/8 D) 1/7
** find the probability that a leap year selected at random will contain;
151) 53 Sundays.
A) 2/7 B) 3/7 C) 1/8 D) 4/7
152) Thursday or 53 Fridays.
A) 1/7 B) 3/7 C) 2/7 D) 4/7
153) 53 Thursday and 53 Fridays
A) 1/7 B) 3/7 C) 2/7 D) 4/7
** In a family there are four children. find the probability that
154) all have different birthdays
A) (364. 363.362)/(365)⁴
B) (365 364. 363.)/(365)³
C) (364. 363.362)/(365)³ D) none
155) exactly two will have different birthdays.
A)(6. 364. 363)/(365)⁴
B)(6.364.362)/(365)³
C)(6. 363.362)/(365)³ D( none
156) at least two will have different birthdays.
A) {364(6.362+4)+1}/(365)³
B){364.363. 369}/(365)⁴
C) {364.363.362}/(365)³ D) none
157) at most two will have same birthday.
A){364.369.362}/(365)³
B) {364.363.369}/(365)⁴
C) {364.363.362}/(365)³ D) none
158) X and Y stand in a line with eight persons. find the probability that are exactly 3 persons between X and Y.
A)3/15 B) 4/15 C) 2/15 D) none
159) 12 persons among home X and Y are included are seated at a round table. find the probability that there are three persons between X and Y.
A) 1/11 B) 3/11 C) 2/11 D) none
* A man has two French, 5 German and 4 Spanish friends. he invites one or more of them in his birthday party. find the probability that there will be:
160) Atleast one German friend.
A) 411/511 B) 448/551
C) 448/511 D) none
161) At least one friend from each country.
A) 310/510 B) 351/551
C) 315/511 D) none
** An URN contains 2 mangoes, 3 apples and 4 oranges. Any number of fruits are selected from it
find the probability that in the selection there will be:
162) at least one mango.
A) 40/59 B) 4/95 C)38/83 D) none
163) at least one fruit of each type
A) 21/59 B) 22/59 C)24/55 D) none
164) a five digit number is to be formed with the digit 0, 1, 2 ,3, 4. find the probability that divisible by 4.
A) 6/16 B) 4/16 C) 5/16 D) none
** A number is drawn at random from the set of numbers 1--15. find the probability that:
165) it is a number more than 4.
A) 9/15 B) 10/15 C) 11/15 D) none
166) it is an even number
A) 7/15 B) 10/15 C) 11/15 D) none
167) it is an odd number
A) 9/15 B) 10/15 C) 8/15 D) none
168) it is an even number greater than 4.
A) 9/15 B) 7/15 C) 5/15 D) none
169) it is an odd number less than 10.
A) 5/15 B) 7/15 C) 9/15 D) none
170) it is a multiple of 3.
A) 9/15 B) 5/15 C) 7/15 D) none
171) It is a multiple of 4.
A) 3/15 B) 6/15 C) 9/15 D) none
172) it is a multiple of 3 and 4.
A) 3/15 B) 10/15 C) 1/15 D) none
173) it is a multiple of 3 or 4.
A) 9/15 B) 10/15 C) 7/15 D) none
174) it is a multiple of 5.
A) 1/15 B) 10/15 C) 11/15 D) none
175) It is a multiple of 3 and 5.
A) 9/15 B) 1/15 C) 11/15 D) none
176) it is a multiple of 3 or 5.
A) 9/15 B) 7/15 C) 5/15 D) none
177) A,B C are mutually exclusive and exhaustive events. find P(B) If 1/8 P(C)= 1/2P(A)= P(B).
A) 1/11 B) 1 C) 2/11 D) none
** can the following represent a measures of probability ?
178) P(A)=0.2, P(B)= 0.7 and P(C)= 0.1
A) Yes B) no C) cannot say D) none
179) P(A)=0.4, P(B)= 0.6 and P(C)= 0.2
A) yes B) no C) neither A nor B
D) can't say
180) P(AUB)=0.5, P(B)= 0.6 and P(C)= 0.2
A) yes B) no C) neither A nor B
D) can't say
**if P(A)=1/4, P(B)= 2/5 and P(AUB)= 1/2, Find
181) P(A^B)
A) 3/20 B) 1/10 C) 1/4 D) 1/2
182) P(A^B')
A) 3/20 B) 1/10 C) 1/4 D) 1/2
183) P(A'^B)
A) 3/20 B) 1/10 C) 1/4 D) 1/2
184) P(A'^B')
A) 3/20 B) 1/10 C) 1/4 D) 1/2
185) P(A'UB)
A) 9/10 B) 7/10 C) 3/10 D)none
186) P(AUB')
A) 2/5 B) 3/5 C) 1/5 D) None
P(A/B)
A) 2/8 B) 5/8 C) 3/8 D) None
187) P(A/B)
A) 2/8 B) 5/8 C) 3/8 D) None
188) P(B/A)
A) 2/5 B) 3/5 C) 1/5 D) None
189) P(A'/B)
A) 5/8 B) 8/5 C) 3/5 D) None
190) P(B'/A)
A) 1/5 B) 2/5 C) 3/5 D) None
191) P(B/A')
A) 2/3 B) 1/3 C) 1/3 D) None
192) P(A'/B')
A) 4/10 B) 5/10 C) 6/10 D) None
193) P(B'/A')
A) 1/3 B) 2/3 C) 4/5 D) None
** Out of the numbers 1 to 120, one is selected at random. what is the probability that it is divisible by:
194) 10 or 13 ?
A) 8/40 B) 7/40 C) 6/40 D) 13/40
195) 8 or 10 ?
A) 8/40 B) 7/40 C) 5/40 D)none
196) A constructive company is bidding for two contracts. A and B. The probability that the company will get contact A is 3/5. The Probability that the company will get contract B is 1/3 and the probability that the company will get both the contracts is 1/8. what is the probability that the company will get at least one contract.
A) 79/120 B) 97/120
C) 89/120. D) none
197) the probability that the contractor will get one electric contract is 3/5, and the probability that the company will not get a plumbing contractor 7/10. if the probability of getting at least one contract is 4/7. what is the probability that he will get both the contracts.
A) 32/70. B)65/70 C)23/70 D) N
198) the probability that a management account's job applicants has a postgraduate degree is 0.30. that he has some work experience as Chief accountant is 0.70 and that he has both is 0.20. Out of 400 applicants, what number would have either a postgraduate degree or some professional work experience or both ?
A) 230 B) 300 C)350 D) 320
199) the probability that a student passes in statistics test is 2/3 and the probability that he passes both statistics and mathematics test is 14/45. the probability that he passes at least one test is 4/5. what is the probability that he passes in mathematics ?
A) 2/9 B) 3/9 C) 4/9 D) 5/9
200) one counter is drawn at random from a bag containing 70 counters marked with the first 70 numerals. find the chance that it is a multiple of 8 or 9.
A) 1/14 B) 2/14 C) 4/14 D) 3/14
201) From a set of 18 balls marked 1,2,3,..... 17,18, one ball is drawn at random. what is the probability that it's number is either a multiple of 3 or 4 ?
A) 0.5 B) 0.67 C) 0.33 D) none
** Three fair coins are tossed once. find the probability of
202) at least one head
A) 1/8 B) 3/8 C) 5/8 D) 7/8
203) exactly one tail.
A) 1/8 B) 3/8 C) 5/8 D) 7/8
204) A bag contains 10 red and 6 green balls. Two successive drawing of three balls are made without replacement. find the probability that the first drawing will give 3 red balls and second will give three green balls.
A) 51/1001 B) 25/1001
C) 51/1000 D) 15/1001
205) A bag contains 6 white and 9 black balls. 4 balls are drawn at a time. Find the probability of the first draw to give 4 white balls and the second to give 4 Black balls when the balls are not replaced before the second draw.
A) 7/315 B) 3/715 C) 6/615 D)none
206) a bag contains 5 red 3 black balls and the second bag on contains 4 red 5 black balls. one of these is selected at random and a draw of two balls is made from it. what is the probability that one of them is a red and the other is black.
A)27/50 B) 75/504 C)275/504 D) N
** A bag contains 4 defective 6 good electronic calculators. They are drawn out by one by one without replacement.
207) what is the probability that the two calculators so drawn are good?
A)1/3. B) 2/3. C) 1/5 D) none
208) One of the calculators so drawn is tested and found to be good. What is the probability that the other one is also good ?
A) 4/9 B) 5/9 C) 7/9 D) none
209) X and Y stands in a line at random with 8 other persons. what is the probability that there are 3 persons between X and Y ?
A) 1/15 B) 3/15 C) 2/15 D) none
210) an article manufactured by a company consists of two parts A and B. In the process of manufacture of part A, 9 out of 100 are likely to be defective. Similarly 5 out of 100 are likely to be defective in the manufacture of part B. Find the probability that the assembled article will not be defective?
A) 0.1355. B) 0.1535
C) 0.1531. D) none
211) there are 4 balls in a bag--- white, red, green and blue. if a ball is drawn out at random 3 times in succession, what is the chance that all the three would be white ?
A) 2/64 B) 1/64 C) 5/64 D) none
212) If a die is thrown twice, what is the chance that first throw does not show less than 4 and the 2nd does not show more than 4?
A) 2/3 B) 1/3 C) 4/5 D) none
***one bag contains 4 red and 2 black balls, another bag contains 3 red and 5 black balls. If one ball is drawn from each bag, determine the probability that ;
213) both are red
A)1/4. B) 1/2 C) 3/4 D) none
214) both are black
A)5/24. B) 7/24 C) 9/24 D) none
215) one is red and one is black.
A) 11/24. B) 13/24
C) 29/24 D)92/192
216) A bag contains 4 green and 6 red balls. A ball is drawn at random and then without replacing it, a second ball is drawn. what is the chance that a green ball is drawn each time?
A)2/15. B) 2/13 C) 2/11 D) none
217) Two drawing each of 4 balls are made from a bag containing 6 red and 5 black balls, the balls not being replaced before the second trial. find the chance that the first Drawing its 4 red balls and the second 1 red and 3 black balls.
A) 3/77 B)4/77 C) 2/77 D) none
*** A problem in statistics is given to the three Students A, B and C whose respective chances of solving are 1/3, 1/4 ,1/5. find the probability that:
218) it is solved by all of them.
A) 1/60 B) 2/5 C) 3/5 D)13/30
219) it is solved by none of them.
A) 1/60 B) 2/5 C) 3/5 D)13/30
220) it is solved.
A) 1/60 B) 2/5 C) 3/5 D)13/30
221) it is solved by exactly one of them.
A) 1/60 B) 2/5 C) 3/5 D)13/30
222) it is solved by exactly two of them.
A) 3/20 B) 2/5 C) 3/5 D)13/30
223) it is solved by at least 2 of them.
A) 2/6 B) 1/6 C) 5/6 D) none
224) it is solved by almost one of them.
A) 5/6 B) 5/7 C) 5/9 D) 5/11
225) a problem in statistics is given to 3 students A, B and C whose chances of solving it are 1/3, 1/4, and 1/5 respectively. what is the probability that the problem will be solved?
A) 2/5 B) 4/5 C) 3/5 D)none
226) the probability of solving a problem by 3 students, A ,B and C, are 2/7, 3/8 and 1/2 respectively. if each of them by independently, find the probability that the problem could not be solved.
A) 52/112. B) 25/111
C) 25/112 D) none
*** The independent probability that the three sections of the costing department will encounter error are 0.1, 0.3 and 0.3, each week respectively. Calculate the probability that there will be:
228) At least one computer error.
A) 0.955. B) 0.459
C) 0.959 D) 0.559
229) One and only one computer error encountered by the costing department.
A) 0.247. B) 0.427
C) 0.924 D) none
*** A bag contains 4 red and 3 blue balls, Two drawings of two balls are made. find the probability of drawing 1st 2 red balls and 2nd 2 blue balls:
229) If the balls are returned to the bag after the 1st draw.
A)2/49 B) 2/47 C) 5/49 D)none
230) if the balls are not returned to the bag after the first draw.
A) 2/25 B) 1/25. C) 3/25 D) none
231)Two urns contains 3 white, 7 red, 15 black and 10 white, 6 red and 9 black balls respectively. one ball is drawn at random from each urn. find the probability that both the balls are of same colour.
A) 702/1624 B) 209/649
C) 207/625 D) 712/925
** If two balls are drawn at random one after the other from a bag containing 3 white and 5 black balls. what is the probability that:
232) the first ball is white.
A) 15/56 B) 17/56 C) 19/56 D) N
233) one ball is white and other is black ?
A) 15/17 B) 15/28 C) 15/29 D) N
234) In a group of equal number of men and women in 10% man & 45% women are unemployed. what is the probability that a person selected at random is employed?
A)39/40 B)19/40 C) 29/40 D)59/60
235) an URN contains 4 white 5 black balls. A second urn contains 5 white and 4 Black balls. one ball is transferred from first urn to the second urn. what is the probability that it is white ?
A) 49/40 B)59/40 C) 69/40 D) N
** an URN contains 2 white and 2 black balls. A second urn contains 2 white and 4 Black balls.
236) one ball is 2000 from each urn, what is the probability that the selected balls will be of the same colour?
A) 0.33 B) 0.50 C) 0.67 D) none
237) if an urn selected at random and one ball is drawn from it. what is the probability that it will be a white ball ?
A) 5/12 B) 6/12 C) 7/12 D) 8/12
238) There are three men aged 60, 65, 70 years. the probability to live 5 years more than age 0.8 for a 60 years old, 0.6 for a 65 years old and 0.3 for a 70 year old person. find the probability that at least two of the three persons will remain alive 5 years hence.
A) 0.216 B) 0.5 C) 0.612 D) none
239) A bag contains 5 white and 4 Black balls. A ball is drawn at random from the bag and put into the another bag, which contains 3 white and 7 black balls. A ball is drawn at random from the 2nd bag. what is the probability that it is white?
A)23/99 B)43/99 C)54/99 D)32/99
240) one shot is fired from each of the three guns. let A , B and C denote the events that the target is hit by the first, second and third gun respectively. Assuming that A, B and C are mutually Independent events and that P(A)= 0.05, P(B)= 0.6 , P(C)= 0.8. find the probability that at least one hits the target.
A)?96 B) 0.69 C) 0.33 D) none
*** Mr X is called for an interview of three separate post. At the first interview there are five candidates, At the second four candidates and at the third 6 candidates. If selection of each candidate is equally likely. find the probability that Mr. X will be selected for;
241) at least one post
A) 0.35 B) 0.55 C) 0.5 D) 0.65
242) at least two posts
A) 1/10 B)13/120
C) 52/120 C) 47/120
243) A bag contains 3 red and 5 white balls and the second bag contains 4 red and 6 white balls. one ball is drawn at random from the first bag and put into the second bag. If now, a ball is drawn from the second bag, find the probability that it is red.
A)35/88 B)53/88 C)16/89 D) n
244) A certain player is known to win the probability 0.3 if the track is fast and 0.4 if the track is slow. For Monday, there is 0.7 probability of fast track 0.3 of a slow track. what is the probability that player X will in Monday ?
A)0.67 B)0.99 C)0.33 D) none
*** A die is loaded in such a way that each odd number is as twice likely to occur as even number. find
245) the probability that the number rolled is a perfect square,
A)0.33 B)0.53 C) 0.43 D) 00.67
246) the probability that the number rolled is a perfect square provided that it is greater than 3.
A)0.22 B) 0.11 C) 0.33 D) 0.54
*** 100 student randomly selected from a group of students are cross classified by age and educational qualification as below:
Qualification Age(yrs) Total
25 & 26-28 over
Under 28
Graduate 24 19 11 54
P-Grad. 11 16 19 46
Total 35 35 30 100
A student is selected at random from group find the probability that:
247) his age is between 26 to 28 years.
A) 0.45 B) 0.25 C) 0.35 D) 0.15
248) he is a graduate.
A) 0.45 B) 0.65 C) 0.85 D) 0.54
249) His age is between 26 to 28 years and he is a graduate.
A) 0.91 B) 0.19 C) 0.54 C) 0.45
250) His age is between 26-28 years assuming that he is a graduate.
A) 0.25 B) 0.15 C) 0.45 D) 0.35
251) He is a graduate that his age between 26 to 28.
A) 0.54 B) 0.45 C) 0.33 D) 0.98
252) A can solve 80% of the problems in statistics and B can solve 70%. what is the probability that at least one of them will solve a problem selected at random ?
A) 0.29 B) 0.18 C) 0.81 D) 0.92
253) How many tosses of a coin is needed so that the probability of getting at least one head is 87.5%?
A) 2 B) 4 C) 3. D) 8
254) In a game of bridge what is the probability that a hand will contains all 4 kings ?
A) 11/4156. B) 11/5146
C) 11/4165 D) none
*** the following table shows the qualification of 100 employees in a firm according to their age and qualification ?
< 30 30-40 >40 Tot
Graduate 10 20 15 45
P.Graduate 15 25 15 55
Total. 25 45 30 100
if an employee selected at random find the probability that:
255) His age is below 30 years,
A) 1/4 B) 1/3. C) 1/2 D) N
256? he is a graduate
A) 8/20 B) 10/20 C) 13/20 D) 9/20
257) He is a postgraduate and his age he is above 40 yrs.
A) 3/20 B) 13/20 C) 17/20 D) 11/20
258) he is postgraduate if it is known that is age between 30 to 40 years.
A) 4/9 B)5/9 C) 7/9 D) none
259) four cards are drawn from a pack of 52 cards. what is the probability that they are from four different suits?
A) 219/2082 B) 2197/20285
C) 2197/20825. D) 2179/20825
260) the first 12 letters of the alphabet written at random. find the probability that there are exactly 4 letters between C and D.
A) 6/66. B) 8/66 C) 7/66 D)13/66
261) the letters of the word EDUCATION are arranged at random. Find the probability that there will be exactly four letters between A and B.
A)1/7 B) 1/3 C) 1/9. D) 1/3
262) from 8 counters marked 1, 2, 3,.......8. 4 counters are selected at random. find the chance of getting one odd and one even count.
A) 31/35 B) 34/35 C) 3/35 D)1/35
263) 40% of students in a class are girls. If 60% and 70% of the boys and girls respectively of the class pass a test. what is the probability that a student selected from this class will have passed the test?
A)16)35 B)15/36 C)61/85 D)53/65
264) In a group of 14 males and 6 females, 8 and 3 of the males and females respectively are aged above 40 years. what is the probability that a person selected at random from his group is aged 40, given that selected person is a female ?
A) 0.29 B) 0.33 C) 0.67 D) 0.50
265) The odds against a certain events are 5:2 and odds in favour of another event, independent of former are, 6:5. find the chance that at least one of the event will happen.
A) 25/77 B)35/77 C)52/77 D)65/77
266) A person is known to hit 4 out of 5 shot, whereas another person is known to hit 3 out of 4 shots. find the probability of hitting a target if they both try.
A) 0.29 B) 0.92 C) 0.95 D) 0.98
267) what is the probability that over a Two day period the number of requests would be either 11 or 12 if at a motor garage the records of service requests along with their probabilities are given below:
Daily Demand : 5 6 7
Probability: 0.25 0.65 0.10
A) 0.7579 B) 0.8589
C) 0.7975 D) 0.7957
** A market research firm is interested in surrveing certain attitudes in a small community. There are 125 households broken according to Income, ownership of a T.V and ownership of a telephone.
Annual inc. Ann. Income
₹18000 or less above 18000
Owner of TV: 27 20 18 10
No of TV set: 18 10 12 10
268) what is the probability of obtaining a TV owner if a household is selected at random ?
A) 0.40 B) 0.60 C) 0.20 D) 0.30
269) If a household has income &18000 and is a telephone subscriber, what is the probability he has a TV?
A) 0.40 B) 0.20 C) 0.60 D) 0.30
270) what is the conditional probability of drawing a household that owns a TV, given that the household owns a TV ?
A) 0.20 B) 0.10 C) 0.50 D) 0.60
271) Are the events 'ownership of a TV' and 'telephone subscriber' independent ?
A) No B) Yes C) Can't say D) none
*** two balance die are thrown together. Write down the sample space. Now find the probability of obtaining:
272) 4 in both dice.
A) 2/18 B) 1/36 C)3/36 D) 7/36
273) Doublets.
A) 5/6 B) 5/36 C) 1/6 D) 1/36
274) 2 in one and 5 in another.
A) 2/36 B) 1/36 C) 15/36 D) 2/18
*** A frequency distribution the weekly wages of 500 workers is given below:
Wages No. of workers
100- 149 21
150- 199 80
200-249 175
250- 299 158
300- 349 55
350- 399 11
Two workers are selected at random. find the probability that the wages of both are:
275) Less than ₹200
A) 101/2945 B) 101/2495
C) 201/2495 D) none
276) equals to or greater than ₹300
A) 924/34950. B) 429/34950
C) 429/24950 D) 924/24950
277) equals to or greater than ₹ 200 but less than ₹300
A) 27639/63275 B) 27639/62375
C) 19857/59847 D) 15987/62357
278) The odds in favour of an event are 4:3. The odds against another independent events are 2:3. what is the probability that atleast one of the event will occur ?
A) 35/36 B) 28/35
C)29/36 D) 29/36
279) The manufacturing process of an article consists of two parts X and 4. the probability of defects in part X and 4 are 10% and 15% respectively. what is the probability that an assembled product will not have any defects ?
A) 0.235 B) 0.325
C) 0.523. D) 0.532
280) A pair of fair dices is thrown. Find the probability of getting a sum of 7, when it is known that the digit in the first die is greater than that of two in a second
A) 0.198 B)0.2 C)0.549 D) 0.259
281) In a single cast with 3 dices, what is the probability of throwing 3 sixes ?
A) 2/216 B)1/108 C)1/216 D)3/126
282) In a single cast with 3 dices, find the chance of getting different digits.
A) 4/9 B) 4/13 C) 5/9. D) 5/13
283) In a single cast with 3 dices, find the probability of getting same digits in two dice and different digit in another.
A) 6/12. B) 5/12 C) 5/13 D) 5/14
284) 5 students A, B, C, D and E occupy their seats at random in a bench. find the probability that the students A and B are not consecutive.
A) 0.55 B) 0.35 C) 0.25 D) 0.6
285) 12 dissimilarity balls are distributed random into 5 boxes A,B,C,D,E. find the probability that these boxes contain respectively 3,4, 1, 4, 0 balls.
A) 136/225 B) 136800/62589
C) 138569/36259. D) none
286) 5 commerce and 4 Science students are arranged at random in a row. find the probability so that the commerce and Science students are placed alternatively?
A)1/216 B)2/216 C)5/216 D)19/216
287) if the number 1, 2, ...., N are arranged in a line at random. what is the probability that the number 1 and 2 will appear to each other?
A) N/2 B) N C) 1/N D) N/9
288) the odds against 2 events are 2:7 and 7:5 respectively. If the events are independent, find the probability that at least one of them will occur ?
A)45/74 B)35/54 C) 45/54 D)47/54
289) A class consists of 30 boys and 20 girls of which half the boys and half the girls have blue eyes.
A)0.75 B)0.98 C) 0.56 D)0.80
*** Two consecutive drawing of a digits are made at random from the number 1, 2, 3, ........, 21. find the probability that the first drawn number is even the second is an odd number. when the First drawn number is
290) Replaced
A) 110/440. B) 110/441
C) 110/442 D) none
291) not replaced before the second drawing.
A) 11/24 B)11/35 C)11/42 D)11/58
292) It is 9 to 5 against a person who is 50 years living till he is 70 and 8 to 6 against a person who is 60 years living till his 80. find the probability that at least one of them will be alive after 20 years.
A)30/49 B)25/64 C)31/64 D)31/49
293) the odds that a book will be favourably reviewed by three independent critics are 5 to 2, 4 to 3, and 3 to 4 respectively. what is the probability that of the three books a majority will be favorable?
A)225/343. B) 209/343
C) 391/400. D) 420/840
*** out of the 20 games of chess played between two players A and B, A 12, B won 4 and 4 ended in a tie. In tournament of three games find the probability that:
294) B wins all the three
A) 2/125 B) 1/125
C) 3/125. D) none
295) B wins at least one
A) 61/125 B) 12/125
C) 88/125. D) 78/125
296) 2 games end in a tie
A) 12/125 B) 21/125
C) 49/125. D) 64/125
297) The probability that a teacher will take a surprise test during any class meeting is 1/5. If a student is absent on two days, what is the probability that he will miss at least one test ?
A) 16/25 B) 1/25
C) 4/125. D) 9/25
298) In number is chosen at random from the first n natural numbers and suppose A and B denotes the events the chosen number is divisible by 2 and 3 respectively A and B are independent if n= ?
A) 96 B) 97. C) 99. D) 100
*** Three lots contain respectively 4%, 5% and 10% defective articles. One article is to chosen at random from each lot. find the probability of getting
299) exactly one defect
A) 0.1868 B) 0.1786
C) 0.1686 D) 0.8816
300) at least one defective article among the three articles drawn
A) 0.9217. B) 0.2917
C) 0.7192 D) 0.1792
301) A pair of dice is thrown. find the probability that the sum is 10 or greater if a 5 appears on the first dice.
A) 0.67 B)0.99 C)1.00 D)0.33
302) In supplies of 3 components viz. base, nack and switch for an electric lamp, the percentage of defective on a day were 5, 20 and 10 respectively. An assembled lamp is considered defective if at least one of the three components is defective. If components are selected randomly, what is the probability that an assembled lamp would be defective ?
A) 79/250. B) 97/250
C) 25/250. D) 129/250
*** 4 balls are drawn from a bag containing 5 black and 8 white balls
Find:
303) All white -against
A) 129:14 B) 14:129
C) 12:138. D) none
304) all black --favour
A) 1:142. B) 145:6
C) 3:139. D) 10:125
305) 2 white and 2 black --favour
A)56:89. B) 56:87
C) 65:78 D) none
306) 1 white and 3 black --against
A) 129:61. B)125:87
C) 654:987. D) 127:16
307) One black and 3 white --favour
A) 56:87 B)56:89
C) 65:78. D)) none
308) What are the against throwing an Ace oor 6 in a single cast with a dice and what are the odds in favour ?
A) 1:3 B) 1:4 C) 2:1 D) 1:2
**** 30% of the students failed in mathematics, 20% in chemistry and 10% in both. find the probability
309) he has failed either in maths or in chemistry.
A) 2/5 B) 3/5 C) 1/5. D) 1/10
310) he has failed neither in maths nor in Chemistry.
A) 2/5 B) 3/5 C) 1/5. D) 1/10
311) He has failed in maths but not in chemistry.
A) 2/5 B) 3/5 C) 1/5. D) 1/10
312) he has failed in chemistry but not in maths.
A) 2/5 B) 3/5 C) 1/5. D) 1/10
313) He has failed in maths known that he has failed in chemistry.
A) 2/5 B) 1/2 C) 1/5. D) 1/10
314) he has failed in chemistry known that he failed in maths
A) 2/5 B) 3/5 C) 1/3. D) 1/9
315) He has failed in maths known that he had not failed in chemistry.
A) 2/5 B) 3/5 C) 1/7. D) 1/4
316) he has failed in chemistry known that he has not failed in maths.
A) 1/7 B) 3/4 C) 1/5. D) 1/10
317) he has not failed in chemistry known that he has failed in maths.
A) 2/5 B) 2/3 C) 1/5. D) 1/10
318) he has not failed in a maths known that he has failed in chemistry.
A) 2/5 B) 3/5 C) 1/5. D) 5/10
319) he has not failed in Chemistry, known that he has not failed in maths.
A) 2/7 B) 3/7 C) 6/7. D) 1/10
320) He has not failed in maths known that he has not failed in chemistry.
A) 2/4 B) 3/4 C) 1/5. D) 1/10
321) A speaks truth in 60% and B in 75% of the cases. In what percentage of cases are they likely to contradict each other in stating the same fact.
A) 0.45 B)0.54 C)0.55 D) 0.65
322) A six faced die is so biased that it is twice likely to show an even number as compared to an odd number when thrown. It is thrown twice. Find the probability that the sum of the faces thrown will be even.
A) 7/9 B) 5/9. C) 8/9 D) 9/9
323) A bag contains 8 red and 5 white balls. two successive drawn of three balls are made without replacement. find the probability that the 1st drawing will give 3 white and second drawing will give 3 red balls.
A) 4/294 B) 7/597
C) 7/429. D) 159/429
324) with respect to the above question, however, if three balls are replaced before second draw, find the probability that first drawing will give 3 White and the second will give 3 red.
A) 140/20449 B) 1598/20449
C) 140/20944 D) None
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