Exercise -A
1) An unbiased dice is thrown. What is the probability of getting:
A) an even number. 1/2
B) a multiple of 3. 1/3
C) an even number or a multiple of 3. 2/3
D) an even number and a multiple of 3. 1/6
E) a number 3 or 4. 1/3
F) an odd number. 1/2
G) A number less than 5. 2/3
H) A number greater than 3. 1/2
I) A number between 3 and 6. 1/3
2) Two unbiased coins are tossed simultaneously. Find the probability of getting:
A) Two heads. 1/4
B) one head. 1/2
C) one tail. 1/2
D) at least one head. 3/4
E) at most one head. 3/4
F) No head. 1/4
3) Three unbiased coins are tossed together. Find the probability of getting:
A) all heads. 1/8
B) two heads . 3/8
C) one head. 3/8
D) at least two heads. 1/2
4) Two dice are thrown simultaneously. Find the probability of getting:
A) an even number as the sum. 1/2
B) the sum as the prime number. 5/12
C) a total atleast 10. 1/6
D) a doublet of even number. 1/12
E) A multiple of 2 on one dice and a multiple of 3 on the other. 11/36
F) same number on the both dice. 1/6
G) a multiple of 3 as the sum. 1/3
5) Find the probability that a leap year selected random, will contain 53 Sundays. 2/7
6) What is the probability that a number selected from the numbers 1,2,3,..... 25 is a prime number, when each of the given numbers is equally likely to be selected. 9/25
7) Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. What is the probability that the ticket has a number which is a multiple of 3 or 7 ? 2/5
8) A pack of playing cards consists of 52 cards, each of the 52 cards being equally likely to be drawn. Find the probability that the card drawn is:
A) An ace. 1/13
B) red. 1/2
C) either red or King. 7/13
D) red and a king. 2/26
E) a face card. 4/13
F) a red face card. 2/13
G) 2 of spade. 1/12
H) 10 of a black suit. 1/26
9) The king queen and jack of clubs are removes from a deck of 52 playing cards and the well shuffled. One card is selected from the remaining cards. Find the probability of getting:
A) A heart. 13/49
B) a king. 3/49
C) a club. 10/49
D) the 10 of Hearts. 1/49
10) A bag contains 3 red and 2 blue marbles. A marble is drawn at random of drawing a blue marble. 2/5
11) A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, Find the number of blue balls in the bag. 10
12) A bag contains 12 balls out of which x are white.
A) If one ball is drawn at random, what is the probability that it will be a white ball. x/12
B) if 6 more white balls are put in the bag, the probability of drawing a white ball will be double than that A. Find x. 3
13) It is know that a box of 600 electric bulbs contains 12 defective bulbs. One bulb is taken out at a random from this box. What is the probability that it is a non defective bulb ? 0.98
14) 17 cards number 1,2,3,....17 are put in a box and mixed thoroughly. One person draws a card from the box. Find the probability the number on the card is :
A) odd. 9/17
B) a prime. 7/17
C) divisible by 3. 5/17
D) divisible by 3 and 2 both. 2/17
15) Cards marked with the numbers 2 to 101 are placed in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is:
A) an even number. 1/2
B) a number less than 14. 3/25
C) a number which is a perfect square. 9/100
D) A prime number less than 20. 2/25
16) 1000 tickets of a lottery were sold and there are 5 prizes on these tickets. If Saket has purchased one lottery ticket, what is the probability of winning a prize ? 0.005
17) A child has a block in the shape of a cube with one letter written on each face as shown
A B C D E A
The cube is thrown once. What is the probability getting
A) A. 1/3
B) D. 1/6
18) A bag contains 5 red balls, 8 white balls, 4 green balls and 7 black balls. If one ball is drawn at random, find the probability that it is:
A) black. 7/24
B) red. 5/24
C) not Green. 5/6
19) A die is thrown. Find the probability of getting:
A) a prime number. 1/2
B) two or four. 1/3
C) a multiple of 2 or 3. 2/3
20) In a simultaneous throw of a pair of dice, find the probability of getting:
A) 8 as the sum. 5/36
B) a doublet. 1/6
C) a doublet of prime numbers. 1/12
D) a doublet of odd numbers. 1/12
E) a sum greater than 9. 1/6
F) an even number on first. 1/2
G) an even number on one and a multiple of 3 on the other. 11/36
H) neither 9 nor 11 as the sum of the numbers on the faces. 5/6
I) a sum less than 6. 5/18
J) a sum less than 7. 5/12
K) a sum more than 7. 5/12
21) Three coins are tossed together. Find the probability of getting:
A) exactly two heads. 3/8
B) at least two heads. 1/2
C) at least one head and one tail. 7/8
22) what is the probability that an ordinary year has 53 Sundays ? 1/7
23) what is the probability that a leap year has 53 Sundays and 53 Mondays. 1/7
24) A and B throw a pair of dice. If A throws 9, find B's chance of throwing a higher number. 1/6
25) Two unbiased dice are thrown. Find the probably that the total of the numbers on the dice is greater than 10. 1/12
26) A card is drawn at random from a pack of 52 cards. Find the probably that the card is drawn is:
A) a black King. 1/26
B) either a black card or a king. 7/13
C) black and a king. 1/26
D) a Jack, Queen or a King. 3/13
E) neither a heart nor a king. 9/13
F) spade or an ace. 9/13
G) neither an ace nor or a king. 11/13
27) In a lottery 50 tickets numbered 1 to 50, one ticket is drawn. Find the probability that the drawn ticket bears a prime number. 3/10
28) An urn contains 10 red and 8 white balls. One ball is drawn at random. Find the probability that the ball drawn is white. 4/9
29) A bag contains 3 red balls, 5 black balls and 4 white balls. A ball is drawn at random from the bag. What is the probably the ball drawn is:
A) white ? 1/3
B) red ? 1/4
C) black ? 5/12
D) not red ? 3/4
30) What is the probability that a number selected from the numbers 1, 2, 3,.....15 is a multiple of 4 ? 1/5
31) A bag contains 6 red, 8 black and 4 white balls. A ball is drawn at random. What is the probability that ball drawn is not black ? 5/9
32) A bag contains 5 white and 7 red balls. One ball is drawn at random. What is the probability that ball drawn is white. 5/12
33) Tickets number from 1 to 20 are mixed up and a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 7 ? 2/5
34) In a lottery there are 10 prizes and 25 blanks. What is the probability of getting a prize. 2/5
35) if the probability of winning a game is 0.3, what is the probability of loosing it. 0.7
36) A bag contains 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is:
A) red. 7/15
B) Black or white. 8/15
C) not black. 2/5
37) A black contains 4 red, 5 black and 6 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is
A) white. 2/5
B) red. 4/15
C) not black. 2/3
D) red or white. 2/3
38) Fill in the blanks:
a) Probability of a sure event is--
b) probability of an impossible event is ____
c) The probability of an event (other than sure and impossible event) lies between ___
d) Every elementary event associated to a random experiment has____ probability.
Answer: 1, 0, 0 and 1 , equal
Continue......
EXERCISE-B
1) Find the probability of getting a head in a toss of an unbiased coin. 1/2
2) In a simultaneous toss of two coins, find the probability of getting:
A) 2 heads. 1/4
B) exactly one head. 1/4
C) exactly 2 tails. 1/4
D) exactly one tail. 1/2
E) no tails. 1/4
3) Three coins are tossed once. Find the probability of getting:
A) all heads. 1/8
B) atleast two heads. 1/2
C) atmost two heads. 7/8
D) no heads. 1/8
E) exactly one tail. 3/8
F) exactly two tails. 3/8
G) a head on first coin.
H) atleast one head and one tail. 3/4
4) A die is thrown. Find the probability of getting:
A) an even number. 1/2
B) a prime number. 1/2
C) a number greater than or equal to 3. 2/3
D) a number less than or equal to 4. 2/3
E) a number more than 6. 0
F) a number less than or equal to 6. 1
G) 2 or 4. 1/3
H) A multiple of 2 or three. 2/3
5). Two dice are thrown simultaneously. Find the probability of getting:
A) an even number as the sum. 1/2
B) the sum as a prime number. 5/12
C) a total of atleast 10. 1/6
D) a doublet of even number. 1/12
E) a multiple of 2 on one dice and a multiple of 3 on the other dice. 11/36
F) same number on both dice. 1/6
G) a multiple of 3 as the sum. 1/3
H) neither a doublet nor a total of 8 will appear. 13/18
I) the sum of the numbers obtained on the two dice is neither a multiple of 2 nor a multiple of 3. 1/3
6) Three dice are thrown together. Find the probability of getting:
A) a total of atleast 6. 103/108
B) a total of 17 or 18. 1/54
7) What is the probability that a number selected from the numbers 1, 2, 3,...., 25, is prime number, when each of the given numbers is equally likely to be selected? 9/25
8) Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random, what is the probability that the ticket has a number which is a multiple of 3 or 7. 2/5
9) A coin is tossed. If head comes up, a die is thrown but if tail comes up, the coin is tossed again. Find the probability of getting:
A) two tails. 1/8
B) head and number 6. 1/8
C) head and an even number. 3/8
10) A letter is chosen at random from the word ASSASSINATION. Find the probability that letter is
A) a vowel. 6/13
B) a consonant. 7/13
11) In a lottery, a person choses six different natural numbers at random from 1 to 20. And if these six numbers match with the six numbers already fixed by the lottery committee, he wins prize. What is the probability of winning the prize in the game? 1/38760
12) On her vacations Ram visits four cities A, B, C , D in a random order. What is the probability that he visits.
A) A before B. 1/2
B) A before B and B before C. 1/6
C) A first and B last. 1/12
D) A either first or second. 1/2
E) A just before B. 1/4
13) A die has two faces each with number '1' three faces each with number '2' and one face with number '3'. If die is rolled once determine:
A) P(2). 1/2
B) P(1 or 3). 1/2
C) P(not 3). 5/6
14) If 4-digit numbers greater than or equal to 5000 are randomly formed from the digits 0, 1, 3, 4 and 7, what is the probability of forming number divisibile by 5 when
A) the digits may be repeated. 2/5
B) the repetation of digits is not allowed. 3/8
15) One card is drawn from a pack of 52 playing cards, each of the 52 cards being equally likely to be drawn. Find the probability that the card drawn is:
A) an ace. 1/13
B) red . 1/2
C) either red or king. 7/13
D) red and a king. 1/26
16) An urn contains 9 red, 7 white and 4 black balls. If two balls are drawn at random, find the probability that:
A) both the balls are red. 18/95
B) one ball is white. 91/190
C) the ball are of the same colour. 63/190
D) one is white and other red. 63/190
17) A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that
A) one is red, one is white and one is blue. 4/17
B) one is red and two are white. 3/68
C) two are blue and one is red. 7/34
D) one is red. 33/68
18) A bag contains 4 red, 7 white and 5 black balls. If two balls are drawn at random, find the probability that
A) both the balls are white. 7/40
B) one is black and the other red. 1/6
C) both the balls are of the same colour. 37/120
19) A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probability that
A) all will be blue. 20C5/60C5
B) at least one will green? 1 - 30C5/69C5
20) A box contains 8 red, 3 white and 9 blue balls. 3 balls are drawn at random, what is the probability that
A) all the three balls are blue balls. 7/95
B) all the balls are of different colours. 18/95
21) A box contains 5 red marbles, 6 white marbles and 7 black marbles. 2 marbles are drawn from the box, what is the probability that both the balls are red or both are black. 31/153
22) In a lottery 10000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy
A) 1 ticket. 999/1000
B) two tickets. 9990C2/10000C2
C) 10 tickets. 9990C10/10000C10
23) The number of lock of a suitcase has 4 wheels, each labelled with ten digits i.e., from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the right sequence to open the suitcase. 1/5040
24) Out of 100 students, two sections of 40 and 60 students are formed. If you and your friends are among the 100 students, what is the probability that
A) you both enter the same section. 17/33
B) you both enter the different sections? 16/33
25) Four cards are drawn at random from a pack of 52 playing cards. Find the probability of getting:
A) all the four cards of the same suit. 198/20825
B) all the four cards of the same number. 13/270725
C) one card from each suit. 2197/20825
D) two red cards and two black cards. (26C2 x 26C2)/52C4.
E) all cards of the same colour. 2.26C4/52C4.
F) all face cards. 12C4/52C4
26) In a lottery of 50 tickets numbered 1 to 50, two tickets are drawn simultaneously. Find the probability that:
A) both the tickets drawn have prime numbers. 21/245
B) none of the tickets drawn has prime number. 17/35
C) one ticket has prime number. 3/7
27) In a lottery, a person chooses six different numbers at random from 1 to 20, and if these six numbers match with six numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game? 1/38760
28) A word consists of 9 letters, 5 consonants and 4 vowels. Three letters are chosen at random. What is the probability that more than one vowel be selected. 17/42
29) Four persons are to be selected at random from a group of 3 men, 2 women and 4 children. Find the probability of selecting:
A) 1 man, 1 woman, 2 children. 2/7
B) exactly 2 children. 10/21
C) 2 women. 1/6
30) A box contains 10 bulbs, of which just three are defective. If a random sample of five bulbs is drawn, find the probabilities that the sample contains:
A) exactly one defective. 5/12
B) exactly two defective. 5/12
C) no defective bulbs. 1/12
31) A box contains 100 bulbs, 20 of which are defective. 10 bulbs are selected for inspection. Find the probability that:
A) all 10 are defective.
B) all 10 are good.
C) atleast one is defective.
D) none is defective.
32) A bag contains tickets numbered 1 to 30. Three tickets are drawn at random from the bag. What is the probability that the maximum number of the selected tickets exceeds 25. 88/203
33) Twelve balls are distributed among three boxes, find the probability that the first box contains three balls. (12C3 x 2⁹)/3¹²
34) Five marbles are drawn from a bag which contains 7 blue and 4 black marbles. Find the probability that:
A) all will be blue. 1/22
B) 3 will be blue and 2 black. 5/11
35) Find the probability that when a hand of 7 cards is dealt from a well shuffled deck of 52 cards. It contains
A) all 4 kings. 1/7735
B) exactly 3 kings. 9/1547
C) atleast 3 kings. 46/7735
36) In a single throw a three dice, determine the probability of getting:
A) a total of 5. 1/36
B) a total of atmost 5. 5/108
C) a total of atleast 5. 53/54
37) Three dice are thrown simultaneously. Find the probability that:
A) all of them show the same face. 1/36
B) all show distinct faces. 5/9
C) two of them show the same face. 5/12
38) What is the probability that in a group of
A) 2 people both will have the same birthday? 1/365
B) 3 people, atleast two will have the same birthday. (364x 363)/365²
39) The letters of the word SOCIETY are placed at random in a row. What is the probability that three vowels come together. 1/7
40) The letters of the word SOCIAL are placed at random in a row. What is the probability that the vowels come together. 1/5
41) The letters of the word CLIFTON are placed at random in a row. What is the probability that the vowels come together. 2/7
42) The letters of the word FORTUNATES are placed at random in a row. What is the probability that the two T come together. 1/
43) The letters of the word UNIVERSITY are placed at random in a row. What is the probability that two I do not come together. 4/5
44) Find the probability that in a random arrangement of the letters of the word UNIVERSITY the two I's come together. 1/5
45) A five digits number is formed by the digits 1,2,3,4,5 without repetition. Find the probability that the number is divisible by 4. 1/5
46) Out of 9 outstanding students in a college, there are 4 boys and 5 girls. A team of four students is to be selected for a quiz programme. Find the probability that two are boys and two are girls. 10/21
47) There are 4 letters and 4 addressed envelopes. Find the probability that all the letters are not dispatched in right envelopes. 23/24
48) The odds in favour of an event are 3:5. Find the probability of occurrence of this event. 3/8
49) The odds in favour of an event are 2:3. Find the probability of occurrence of this event. 2/5
50) The odds in against of an event are 7:9. Find the probability of non-occurrence of this event. 7/16
51) A card is drawn from an ordinary pack of 52 cards and a gambler bets that, it is a spade or an ace. What are the odds against his winning this bet. 9:4
52) Two dice are thrown. Find the odds in favour of getting the sum
A) 4. 1:11
B) 5. 1:8
C) What are the odds against getting the sum 6? 31:5
53) What are the odds in favour of getting a spade if the card drawn from a pack of cards ? What are the odds in favour of getting a king ? 1:3, 1:12
54) A fair coin with 1 marked on one face and on the other and a fair die are both tossed, find the probability that the sum of numbers that turns up is
A) 3. 1/12
B) 12. 1/12
55) In a relay race there are five teams A, B, C, D and E.
A) what is the probability that A, B and C finish first, second and third respectively. 1/60
B) what is the probability that A, B and C are first three to finish (in order). 1/19
56) In shuffling a pack of 52 playing cards, four are accidently dropped; find the probability that the missing cards should be one from each suit. 2197/20825
57) Five cards are drawn from a pack of 52 cards. What is the probability that these 5 will contain
A) just one ace. 3243/10829
B) atleast one ace.
58) If a letter is chosen at random from the English alphabet, find the probability that the letters.
A) a vowel. 5/26
B) a constant. 21/26
59) A class consists of 10 boys and 8 girls. Three students are selected at random. What is the probability that the selected group has
A) all boys. 5/34
B) all girls. 7/102
C) 1 boy and 2 girls. 35/102
D) atleast one girl. 29/34
E) at most one girl. 10/17
Formula:
* (Addition theorem for two events) If A and B are two events associated with a random experiment, then
1) P(A∪B) = P(A) + P(B) - P(A∩B)
* If A and B are mutually exclusive events, then
P(A∩B) = 0
So, P(A UB) = P(A) + P(B)
This is the addition theorem for mutually exclusive events.
2) (Addition Theorem for three events) If A, B, C are three events associated with a random experiment, then
P(A∪B∪C) = P(A) + P(B) + P(C) - P(A∩B) - P(B∩C) - P(A∩C) + P(A∩B∩C).
* If A, B, C are mutually exclusive events, then
P(A∩B)= P(B∩C) = P(A∩C) = P(A∩B∩C) = 0.
P(A U BU C)= PA) + P(B)+ P(C).
This is the addition theorem for three mutually exclusive events.
3) i) P(A'∩B)= P(B) + P(A∩B)
ii) P(A∩B') =P(A) - P(A∩B)
iii) P(A∩B') U P(A'∩B) = P(A) + P(B) - 2P(A∩B)
* P(A'∩B) is known as the probability of occurrence of B only.
* P(A∩B') is known as the probability of occurrence of A only.
* P(A∩B')U P(A'∩B) is known as the probability of occurrence of exactly one of two events A and B.
* If A and B are two events associated to a random experiment such that A ⊂ B, then A' ∩ B ≠ ∅
4) For any two events A and B
P(A ∩ B) ≤ P(A) ≤ P(A U B) ≤ P(A) + P(B).
5) P(A) + P(B) - P(A UB)) = P(A U B) - P(A ∩B).
6) P(A' ∩ B') = 1 - P(A U B)
+++++++++++++++++++++++++++
1) Given P(A)= 3/5 and P(B) = 1/5, Find P(A or B), if A and B are mutually exclusive events. 4/5
2) A and B are two mutually exclusive events of an experiment. If P(not A)= 0.65, P(A UB)= 0.65 and P(B)= p, find the value of p. 0.30
3) Given P(A)= 1/4 and P(B) = 2/5, P(A U B) = 1/2, find
A) P(A∩ B). 3/20
B) P(A∩ B'). 1/10
if A and B are mutually exclusive events.
4) If E and F are two events such that P(E)= 1/4, P(F)= 1/2 and P(E and F)= 1/8, find
A) P(E or F).
B) P(not E and not F)
5) If A and B are two events associated with a random experiment such that P(A)= 0.3, P(B) = 0.4, P(A U B) =0.5, find
A) P(A∩ B). 0.2
6) If A and B are two events associated with a random experiment such that P(A)= 0.5, P(B) = 0.3,P(A∩ B)=0.2, find
A) P(A U B). 0.6
7) If A and B are two events associated with a random experiment such that P(AU B)= 0.8, P(A ∩B) = 0.3, P(A')= 0.5,
find P(B). 0.6
8) Given P(A)= 1/2 and P(B) = 1/3, Find P(A or B), if A and B are mutually exclusive events. 5/6
9) Given P(A)= 0.4 and P(B) = 0.5, if A and B are mutually exclusive events associated with a random experiment. Then find
A) P(AU B). 0.9
B) P(A' ∩ B'). 0.1
C) P(A' ∩ B). 0.5
D) P(A ∩ B'). 0.4
10) A and B are two events such that Given P(A)= 0.54 and P(B) = 0.69, P(A ∩ B) = 0.35. find
A) P(AU B). 0.88
B) P(A' ∩ B'). 0.12
C) P(A ∩ B'). 0.19
D) P(B ∩ A'). 0.34
11) Fill in the blanks:
P(A) P(B) P(A ∩ B) P(AU B)
A) 1/3 1/5 1/15 ____
B) 0.35 ___ 0.25 0.6
C) 0.5 0.35 ___ 0.7
12) Check whether the following probabilities P(A) and P(B) are consistently defined:
A) P(A) = 0.5, P( B)=0.7, P(A ∩ B)= 0.6.
B) P(B)= 0.5 P(B)= 0.4, P(A U B)= 0.85.
13) Events E and F are such that P(not E or not F)= 0.25, State whether E and F are mutually exclusive.
14) A, B, C are three mutually exclusive events associated with a random experiment. Given P(B)= 3/2 P(A), P(C)= 1/2 P(B),
find P(A). 4/13
15) A, B, C are events such that P(A)= 0.3, P(B)= 0.4, P(C)= 0.8, P(A ∩ B) = 0.08, P(A ∩ C) = 0.28, P(A ∩ B∩ C)= 0.09. if P(A U B UC)≥ 0.75, then show that P(B ∩ C) lies in the interval (0.23, 0.48).
16) The probability of two events A and B are 0.25 and 0.50 respectively. The probability of their simultaneously occurance is 0.14. find the probability that neither A nor B occurs.
17) There are three events A, B and C one of which must and only one can happen, the odds are 8 to 3 against A, 5 to 2 against B, find the odds against C. 43:34
18) In a race, the odds in favour of horses A, B, C , ad are 1:3,1:4,1:5,1:6 respectively. Find probability that one of them wins the race. 319/420
19) in an easy competition, the odds in favour of competition P, Q, R, S are 1:2,1:3,1:4,1:5 respectively. Find the probability that one of them wins the competition. 114/120
20) A card is drawn at random from a well shuffled deck of 52 cards. Find the probability of its being a spade or a king. 4/13
21) A card is drawn from a deck of 52 cards. Find the probability of getting an ace or a spade card. 4/13
22) A card is drawn from a deck of 52 cards. Find the probability of getting spade or a king. 4/13
23) Four cards are drawn from a deck of 52 cards. Find the probability that all the drawn cards are of the same colour. 92/883
24) Two cards is drawn from a deck of 52 cards. Find the probability that either both are black or both are kings. 55/211
25) Two card are drawn from a deck of 52 cards. Find the probability that 2 cards drawn are either aces or black cards. 55/21
26) A card is drawn from a pack of 52 cards. Find the probability of getting a king or a heart or a red card. 7/13
27) Four cards are drawn at a time from a pack of 52 cards. Find the probability of getting all the four cards of the same suit. 44/4165
28) Two cards are drawn from a pack of 52 cards. What is the probability that either both are red or both are kings. 55/221
29) In a single throw of two dice, find the probability that neither a doublet nor a total of 9 will occur. 13/1
30) A die is thrown twice. What is the probability that atleast one of the two throws come up with the number 3 ? 11/36
31) Find the probability of getting an even number on the first die or a total of 8 in a single throw of two dice. 5/9
32) A die is thrown twice. What is the probability that atleast one of the two throws comes up with the number 4 ? 11/36
33) Two dice are thrown together. What is the probability that the sum of the numbers on the two faces is neither divisibile by 3 nor by 4 ? 4/9
34) Two dice are thrown together. What is the probability that the sum of the numbers on the two faces is divisible by 3 or 4? 5/9
35) A die has two faces with number '1' three faces each with number '2' and one face with number '3'. If the die is rolled once, determine
A) P(1). 1/3
B) P(1 or 3). 1/2
C) P(not 3). 5/6
36) A natural number is choosen at random from amongst first 500. What is the probability that the number so chosen is divisible by 3 or 5? 233/500
37) One number is chosen from numbers 1 to 100. Find the probability that it is divisible by 4 or 6. 33/100
38) An integer is chosen at random from first 200 positive integers. Find the probability that the Integer is divisible by 6 or 8. 1/4
39) An integer is chosen at random from the numbers ranging from 1 to 50. What is the probability that the Integer chosen is a multiple of 2 or 3 or 10? 33/50
40) Find the probability of at most two tails or atleast two heads in a toss of three coins. 7/8
41) One number is chosen from numbers 1 to 200. Find the probability that it is divisible by 4 or 6? 67/200
42) 100 students appeared for two examinations. 60 passed the first, 50 passed the second and 30 passed both. Find the probability that a student selected at random has passed atleast one examination. 4/5
43) A box contains 10 white, 6 red and 10 black balls. A ball is drawn at random from the box, what is the probability that the ball drawn is either white or red ? 8/13
44) A box contains 6 red, 4 white and 5 black balls. A person draws 4 balls from the box at random. Find the probability that among the balls drawn there is atleast one ball of each colour. 48/91
45) The probability that a person will travel by plane is 3/5 and that he will travel by train is 1/4. What is the probability that he(she) will travel by plane or train. 17/20
46) A box contains 30 bolts and 40 nuts. Half of bolts and half of the nuts are rusted. If two items are drawn at random, what is the probability that either both are rusted or both are bolts.
47) A drawer contains 50 bolts and 150 nuts. Half of the bolts and half of the nuts are rusted. If one item is chosen at random, what is the probability that it is rusted or a bolt ? 5/8
48) Find the probability of getting 2 or 3 tails when a coin is tossed four times. 5/8
49) In an entrance test that is graded on the basis of two examinations, the probability of a randomly selected student passing the first examination is 0.8 and the probability of passing the second examination o.7. the probability of passing atleast one of them is 0.95. What is the probability of passing both. 0.55
50) The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. if the probability of passing the Hindi examination. 0.65
51) A basket contains 20 apples and 10 oranges out of which 5 apples and 3 oranges are defective. If a person takes out 2 at random what is the probability that either both are apples or both are good. 316/435
52) The probability that a person will get an electric contact is 2/5 and the probability that he will not get plumbing contract is 4/7. If the probability of getting atleast one contract is 2/3, what is the probability that he will get both ? 17/105
53) The probability that a student will receive A, B, C or D grade are 0.40, 0.35, 0.15 and 0.10 respectively. Find the probability that a student will receive
A) B or C grade. 0.50
B) at most C grade. 0.25
54) Let A, B and C be three events. If the probability of occuring exactly one event out of A and B is 1 - x, out of B and C is 1 - 2x, out of C and A is 1 - x, and that of occuring three events simultaneously is x², then prove that the probability that atleast one out of A,B, C will occur is greater than 1/2.
55) The probability that a patient visiting a dentist will have a tooth extracted is 0.6, the probability that he will have a cavity filled is 0.2 and the probability that he will have a tooth extracted as well as cavity filled is 0.03. what is the probability that a patient has either a tooth extracted or a cavity filled? 0.23
56) The probability that a patient visiting a dentist will have a tooth cleaned is 0.44, the probability that he will have a cavity filled is 0.24 and the probability that he will have a tooth cleaned as well as cavity filled is 0.60. what is the probability that a patient has either a tooth cleaned or a cavity filled? 0.08
57) Probability that Ram passes in mathematics is 2/3 and the probability that he passes in English is 4/9. If the probability of passing both courses is 1/4, what is the probability that Ram will pass in atleast one of these subjects? 31/36
58) In a town of 6000 people 1200 are over 50 years old and 2000 are female. It is known that 30% of the females are over 50 years. What is the probability that a random chosen individual from the town either female or over 50 years. 13/30
59) Two students Ram and Shyam appeared in an examination. The probability that Ram will qualify the examination is 0.05 and that of shyam will qualify the examination is 0.10. the probability that both will qualify the examination is 0.02. find the probability that:
A) both Ram and Shyam will not qualify the exam. 0.87
B) atleast one of them will not qualify. 0.98
C) only one of them will qualify the exam. 0.11
60) In class XII of a school, 40% of the students study Mathematics and 30% study biology. 10% of the class study both mathematics and biology. If a student is selected at random from the class, find the probability that he will be studying mathematics or biology or both. 3/5
61) In a class of 60 students 30 played football, 32 played cricket and 24 played both football and cricket. If one of these students is selected at random, find the probability that:
A) the student played for football or cricket. 19/30
B) the student has played neither football nor cricket. 11/30
C) the student has played football but not cricket. 2/15
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