TYPE -1
Exercise -1
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2) Two coins are tossed once. find the probability of:
A) getting two heads. 1/4
B) getting at least one head. 3/4
C) getting no head. 1/4
D) getting 1 head and 1 tail. 1/2
3) Three unbiased coins are tossed once. What is the probability of getting
A) all heads. 1/8
B) Two heads. 3/8
C) one head. 3/8
D) at least one head. 7/8
E) at least two heads. 1/2
4) A dice is tossed once. What is the probability of getting:
A) the number 4 ? 1/6
B) an even number. 1/2
C) a number less than 5. 2/3
D) a number greater than 4. 1/3
E) the number 8. 0
F) a number less than 8. 1
5) In a single throw of two dice, find the probability of obtaining a total of eight. 5/36
6) two dice are thrown simultaneously. find the probability of getting:
A) a doublet. 1/6
B) an even number as the sum. 1/2
C) A prime number as sum. 5/12
D) a multiple of 3 as the sum. 1/3
E) a total of at least 10. 1/6
F) a doublet of even numbers. 1/12
G) a multiple of 2 on one die and a multiple of 3 on other die. 11/36
7) 20 cards are numbered from 1 to 20. One card is then drawn at random what is the probability that the number of the card drawn is:
A) a prime number. 2/5
B) an odd number. 1/2
C) a multiple of 5 ? 1/5
D) not divisible by 3 ? 7/10
8) From a well shuffled deck of 52 cards, a card is drawn at random. find the probability of getting:
A) an Ace. 1/4
B) a heart. 1/4
C) an eight of Hearts. 1/52
D) a club. 1/4
E) a red card. 1/2
F) a face card. 3/13
G) a diamond. 1/4
H) a Jack. 1/13
I) a black card. 1/2
9) From a well shuffled deck of 52 cards, a card is drawn at random. Find the probability that the card is drawn is:
A) red and a king. 1/26
B) either red or a king. 7/13
10) a bag contains 9 red and 12 white balls. One ball is drawn at random, find the probability that the ball drawn is red. 3/7
11) If the probability of the occurrence of a certain event M is 3/11, find
A) the odds in favour of its occurrence. 3:8
B) the odds against its occurrence. 8:3
12) The odds in favour of occurrence of an event is 5:12. Find the probability of the occurrence of this event. 5/17
13) If 3/10 is the probability of that an event will happen, what is the probability that will not happen? 7/10
14) three dice are thrown together. find the probability of getting a total of at least 6. 103/108
15) if the odds in favour of an event be 3/5, find the probability of the occurrence of the event. 3/8
16) Two dice are thrown. find
A) the odd in favour of getting the sum 5,. 1:8
B) the odds against getting the sum 6. 31:5
17) a card is drawn from a well shuffled Deck of 52 cards. find
A) the odds in favour of getting a face card,. 3:10
B) the odds against the getting a spade. 3:1
18) Two cards are drawn at random from a pack of 52 cards. What is the probability that both the drawn cards are Aces? 1/221
19) a coin is tossed once. find the probability of getting a tail. 1/2
20) a dice is thrown. find the probability of:
A) getting a 5. 1/6
B) getting a 2 or a 3. 1/3
C) getting an odd number. 1/2
D) getting a prime number. 1/2
E) getting a multiple of 3. 1/3
F) getting a number between 3 and 6. 1/3
21) In a single throw of two dice, find the probability of
A) getting a sum less than 6. 5/18
B) getting a doublet of odd numbers. 1/12
C) getting the sum as prime number. 5/12
22) in a single throw of two dice, find
A) P(an odd number of the first die and a 6 on the second). 1/12
B) P(a number greater than 3 on each die). 1/4
C) P(a total of 10). 1/12
D) P(a total greater than 8). 5/18
E) P(a total of 9 or 11). 1/6
23) a bag contains 4 white and 5 black balls. A ball is drawn at random from the bag. find the probability that the ball drawn is white. 4/9
24) An urn contains 9 red, 7 white and 4 Black balls. A ball is drawn at random. find the probability that the ball drawn is :
A) red. 9/20
B) white. 7/20
C) red or white. 4/5
D) white or black. 11/20
E) not white. 13/20
25) in a lottery, there are 10 prizes and 25 blank. find the probability of getting a prize. 2/7
26) if there are two children in a family, find the probability that there is at least 1 boy in the family. 3/4
27) three unbiased coins are tossed once. find the probability of getting
A) exactly 2 tails. 3/8
B) exactly one tail. 3/8
C) at most two tails. 7/8
D) at least two tails. 1/2
E) atmost 2 tails or atleast 2 heads. 7/8
28) In a single throw of two dice, determine the probability of not getting the same number on the tow dice. 5/6
29) If a letter is chosen at random from the English alphabet, find the probability that the letter chosen is
A) a vowel. 5/26
B) a constant. 21/26
30) a card is drawn at random from a well shuffled pack of 52 cards. What is the probability that the card a number greater than 3 and less then 10 ? 6/13
31) tickets numbered from 1 to 12 are mixed up together and then a ticket is withdrawn at random. find the probability that the ticket has a number which is a multiple of 2 or 3. 2/3
32) What is the probability that an ordinary year has 53 Tuesday? 1/7
33) what is the probability that a leap year has 53 Sundays? 2/7
33) what is the probability that in a group of two people, both will have the same birthday, assuming that there are 365 days in a year and no one has/her birthday on 29 th February? 1/365
34) which of the following cannot be probability of occurrence of an event ?
A) 0 B) -3/4 C) 3/4 D) 4/3
35) If 7/10 is the probability of occurrence of an event, what is the probability that it does not occur ? 3/10
36) The odds in favour of the occurrence of an event are 8:13. find the probability that the event will occur. 8/21
37) The odds in favour of the occurrence of an event are 8:13. find the probability that will occur. 7/11
38) If 5/14 is the probability of occurrence of an event, find
A) the odds in favour of its occurrence. 5:9
B) the odds against its occurrence. 9:5
39) Two dice are thrown, find
A) the odds in favour of getting the sum 6. 5:31
B) the odds against getting the sum 7. 5:1
40) A combination lock on a suitcase has 3 wheels, each labelled with 9 digits from 1 to 9. If an opening combination is a particular sequence of three digits with no repeats, what is the probability of a person guessing the right combination ? 1/504
41) In a lottery, a person chooses six different numbers of random from 1 to 20. If these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize. What is the probability that he wins the prize in the game? 1/38760
42) In a single throw of three dice, find the probability of getting
A) a total of five. 1/36
B) a total of atmost 5. 5/108
Exercise--2
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1) 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 obtaining:
A) two tails. 1/8
B) head and number 6. 1/8
C) head and an even number. 3/8
2) A letter is chosen at random from the word ' ASSASSINATION' find the probability that the letter is
A) a vowel. 6/13
B) a consonant. 7/13
3) In a lottery, a person choses six 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 the prize. what is the probability of winning the prize in the game ? 1/38760
4) On her vacation Veena visits four cities A,B,C,D in a random order, what is the probability that she 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 ? 1/4
5) A die 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
6) If 4-digit numbers greater than or equal to 5000 a randomly formed from the digit 0, 1,3,4 and 7, what is the probability of forming number divisible by 5 when
A) the digits may be repeated. 2/5
B) the repetition of digits is not allowed. 3/8
7) A urn contains 9 red, 7 white and 4 Black balls. If two balls are drawn at random, find the probability that:
A) both the ball are red, 18/95
B) one ball is white. 91/190
C) the balls are of the same colour.
63/190
D) one is white and other is red.
63/190
8) 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 be green. 1 - ³⁰C₅/⁶⁰C₅
9) In a lottery 10000 tickets are sold and 10 equal prizes are awarded. what is the probability of not getting a prize if you buy
A) one ticket. 999/1000
B) two ticket. ⁹⁹⁹⁰C₂/¹⁰⁰⁰⁰C₂
C) 10 tickets. ⁹⁹⁹⁰C₁₀/¹⁰⁰⁰⁰C₁₀
10) The number of lock of suitcase a four wheels, each labelled with 10 digits (from 0 to 9). The lock opens with a sequence of 4 digits with no repeats. what is the probability of getting the right sequence to open the suitcase. 1/5040
11) Three letters are dictated to three persons and an envelop is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. find the probability that at least one letter is in its proper envelope. 2/3
12) Out of 100 students, two sections of 40 and 60 students are formed. if you and our friends are among the hundred students, what is the probability that
A) you both enter the same section ? 17/33
B) you both enter the different sections? 16/33
13) 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 are the same number. 13/270725
C) one card from each suit. 2197/20825
D) two red cards and two black cards. 325/833
E) all cards are of same colour. 92/833
F) all face cards. 99/54145
14) 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 will be selected? 17/42
15) 4 persons are to be chosen at random from a group of 3 men, 2 women and 4 children. find the probability of selecting :
A) 1 man, 1 woman and 2 children. 2/7
B) exactly 2 children. 10/21
C) 2 women. 1/6
16) A box contains 10 bulbs, of which just three are defective. If a random sample of five bulbs are drawn, find the probability that the sample contains:
A) exactly one defective. 5/12
B) exactly two defective. 5/12
C) No defective bulbs. 1/12
17) 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 exceed 25? 88/203
18) 12 balls are distributed among 3 Boxes, find the probability that the first box will contain 3 balls. 110x2⁹/3¹²
19) find the probability that birth days of six different persons will fall in exactly two calendar months. 341/12⁵
20) 5 marbles are drawn from a bag which contains 7 blue marbles and 4 black marbles. what is the probability that:
A) all will be blue? 1/22
B) 3 will be blue and 2 black? 5/11
21) 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 Three Kings. 9/1547
C) at least three kings. 46/7735
22) In a single throw of dice, determine the probability of getting
A) a total of 5. 1/36
B) a total of at most 5. 5/108
C) a total of atleast 5. 53/54
23) 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
24) what is the probability that in a group of
A) two people, both will have the same birthday? 1/365
B) 3 people, at least two will have the same birthday ? 364x363/365
25) The letters of the word SOCIETY are placed at random in a row. what is the probability that three vowels comes together? 1/7
26) Find the probability that in a random arrangement of the letters of the word UNIVERSITY the two I's come together. 1/5
27) A digit 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
28) Out of 9 standing 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
29) In a lottery of 12 microwave ovens, there are 3 defective units. A person has ordered 4 of these units and since each is identically packed, the selection will be random. What is the probability that
A) all 4 units are good. 14/55
B) exactly 3 units are good. 28/55
C) at least 2 units are good. 54/55
30) There are 4 letters and 4 addressed envelopes. find the probability that all the letters are displaced in right envelopes. 23/24
31) the odd in favour of an event are 3:5. find the probability of occurrence of this event. 3/8
32) A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed, find the probability that the sum of the numbers that turns up is
A) 3. 1/12
B) 12. 1/12
33) In a relay race there are five teams A,B,C,D, 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 to finish (in any order). 1/10
34) 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
35) In a single throw of three dice, find the probability of getting a total of 17 or 18. 1/54
36) Three coins are tossed together. find the probability of getting:
A) exactly 2 heads. 3/8
B) at least two heads. 1/2
C) at least one head and one tail. 3/4
37) what is the probability that a leap year has 53 Sundays and 53 Monday . 1/7
38) A and B throw a pair of dice. If A throws 9, find B's chance of throwing a higher number. 1/6
39) In a single throw of three dice, find the probability of getting the same number on all the three dice. 1/36
40) In shuffling a pack of 52 playing cards, four are accidently dropped, find the chance that the missing cards should be one from each suit. 2197/20825
41) ticket numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. what is the probability that the tickets has a number which is a multiple of 3 and 7 ? 2/5
42) A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that:
A) both the balls are white. 7/40
B) one ball is black and the other red. 1/6
C) both the balls are of the same colour. 37/120
43) A bag contains 6red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that:
A) one is red and two are white. 3/68
B) two are blue and one is red. 7/34
C) one is red. 33/68
44) Five cards are drawn from a pack of 52 cards. What is chance that these 5 will contain
A) just one ace. 3243/10829
B) atleast one ace?
45) The face cards are removed from a full pack, Out of the remaining 40 cards, 4 are drawn at random. What is the probability that they belong to different suits ? 1000/9139
46) A box contains 100 bulbs, 20 of which are defective. 10 bulbs are selected for inspection. find the probability that:
A) all 10 a defective. ²⁰C₁₀/¹⁰⁰C₁₀
B) all 10 are good. ⁸⁰C₁₀/¹⁰⁰C₁₀
C) at least one is defective. 1 - ⁸⁰C₁₀/¹⁰⁰C₁₀
D) none is defective. ⁸⁰C₁₀/¹⁰⁰C₁₀
47) find the probability that in a random arrangement of the letters of the word SOCIAL vowels come together. 1/5
48) The letters of the word FORTUNATES are arranged at random in a row. what is the dance that the two 'T' come together. 1/5
49) The letters of the word CLIFTON are placed at random in a row. What is the probability that two vowels come together? 2/7
50) find the probability that in a random arrangement of the letters of the word UNIVERSITY. the two 'I's do not come together. 4/5
51) If odds in favour of an event be 2 : 3, find the probability of occurrence of this event. 2/5
52) If odds against an event is 7:9, find the probability of non-occurrence of this event. 7/16
53) Two balls are drawn at random from a bag contains 2 white, 3 red, 5 green and 4 Black balls, one by one without, replacement find the probability that both the balls are of different colours. 0.78
54) Two unbiased dice are thrown. find the probability that:
A) neither a doublet nor a total of 8 will appear. 13/18
B) the sum of the numbers obtained on the two dice is neither a multiple of 2 nor a multiple of 3. 1/3
55) A bag contains 8 red, 3 white and 9 blue balls. If three balls are drawn at random, determine the probability that
A) all the three balls are Blue Balls.
7/95
B) all the balls of different colours.
18/95
56) A bag contains 5 red, 6 white and 7 black balls. two balls are drawn at random. what is the probability that both balls are red or both are black ? 31/153
57) If a letter is chosen at random from the English alphabet, find the probability that the letter is
A) a vowel. 5/26
B) a constant. 21/26
58) In a lottery, a person chooses 6 different numbers at random from 1 to 20, and if these 6 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
59) 20 cards numbered from 1 to 20. one card is drawn at random. what is the probability that the number on the card is:
A) a multiple of 4 ? 1/4
B) not a multiple of 4 ? 3/4
C) odd ? 1/2
D) greater than 12? 2/5
E) divisible by 5 ? 1/5
F) not a multiple of 6 ? 17/20
60) Two dice are thrown. Find the odds in favour of getting the sum
A) 4. 1:11
B) 5 . 1:8
C) what is the odds against getting the sum 6? 31:5
61) what are the odds in favour of getting a spade if the card drawn from a well shuffled deck of cards ?
What are the odds in favour of getting a king ? 1:3, 1:12
62) a box contains 10 red Marbles, 20 blue Marbles and 30 green Marbles. 5 marbles are drawn at random. From the box, what is the probability that:
A) all are blue? 34/11977
B) at least one is green? 4367/4484
63) A box contains 6 red marbles numbered 1 through 6 and 4 white marbles numbered from 12 through 15. Find the probability that a marble drawn is
A) white. 2/5
B) white and odd number. 1/5
C) even numbered. 1/2
D) red or even numbered. 4/5
64) A class consists of 10 boys and 8 girls. Three students are selected at random. what is the probability that selected group has
A) all boys ? 5/34
B) all girls ? 7/102
C) 1 boy 2 girls ? 35/102
D) at least one girl ? 29/34
E) at most 1 girl? 10/17
65) Five cards are drawn from a well shuffled pack of 52 cards. find the probability that all the five cards are hearts. 33/66640
66) a bag contains tickets numbered from 1 to 20. Two tickets are drawn. find the probability that
A) both the tickets are prime numbers and them. 14/95
B) on one there is a prime number and on the other there is a multiple of 4. 4/19
67) An urn contains 7 white, 5 black balls and 3 red balls. two balls are drawn at random. find the probability that:
A) both the balls are red. 1/35
B) one ball is red and the other is black? 1/7
C) one ball is white. 8/15
68) A committee of two person is selected from 2 men and 2 women. what is the probability that the committee will have
A) no man? 1/6
B) one man ? 2/3
C) two man ?
69) There are 4 men and 6 women on the City Councils. If one Council member is selected for a committee at random, how likely is that it is a woman ? 3/5
TYPE-2
Exercise -1
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1) If A and B are two events associated with a random experiment such that P(A)= 0.35, P(A or B)= 0.85 and P(A and B)= 0.15, find P(B). 0.65
2) Two dice are tossed together. Find the probability of getting a doublet or a total of 6. 2/9
3) In a single throw of two dice, find the probability that neither a doublet nor a total of 10 will appear. 7/9
4) A natural number is chosen at random from among the first 500. What is the probability that the number so chosen is divisible by 3 or 5 ? 233/500
5) 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
6) two cards are drawn at random from a well shuffled pack of 52 cards. What is the probability that either both are red or both are kings. 55/221
7) A box contains 100 bolts and 50 nuts. It is given that 50% bolts and 50% nuts are rusted. Two objects are selected from the box at random. find the probability that either both are bolts or both rusted. 0.58
8) If A and B are two events such that P(A)= 0.5, P(B)= 0.4 and P(A and B)= 0.1. Find
A) P(A or B). 0.7
B) P(A but not B). 0.4
C) P(B but not A). 0.2
D) P(neither A nor B). 0.3
9) the probability that at least one of the event A and B occurs is 0.6. if the probability of simultaneous occurrence of A and B is 0.2, find P(A') + P(B'). 1.2
10) The probability of the occurrence of two events A and B are 0.25 and 0.50 respectively. The probability of their simultaneously occurrence is 0.14. find the probability that neither A nor B occurs. 0.39
11) A card is drawn from a deck of 52 cards. find the probability of getting a king or heart or a red card.
7/13
12) If A and B are two events associated with the random experiment for a which P(A)= 0.60, P(A or B)= 0.85 and P(A and B) =0.42, find P(B). 0.67
13) let A and B be two events associated with random experiment for which P(A)= 0.4, P(B)= 0.5 and P(A or B)= 0.6. find P(A and B). 0.3
14) In a random experiment, let A and B be events such that P(A or B)= 0.7, P(A and B)= 0.3 and P(A')= 0.4. Find P(B). 0.4
15) if A and B are two events associated with the random experiment such that P(A)= 0.25, P(B)= 0.4 and P(A or B)= 0.5, Find the values of
A) P(A and B). 0.15
B) P(A and B'). 0.1
16) If A and B be two events associated with a random experiment such that P(A)=0.3, P(B)= 0.2 and P(A or B)=0.1. find
A) P(A' or B). 0.1
B) P(A or B'). 0.2
17) if A and B are two mutually exclusive events such that P(A)= 1/2 and P(B)=1/3. Find P(A or B). 5/6
18) let A and B to B mutually exclusive events of a random experiment such that P(not A)= 0.65 and P(A or B)=0.65, find P(B). 0.3
19) A, B, C are three mutually exclusive and exhaustive events associated with a random experiment. If P(B)=3/2 P(A) and P(C)=12P(B), find P(A). 4/13
20) the probability that a company executive will travel by plane is 2/5 and that he will travel by train is 1/3. find the probability of his traveling by plane or train. 11/15
21) From a well shuffled pack of 52 cards, a card is drawn at random. find the probability of its being a king or queen. 2/13
22) from a well shuffled pack of cards, a card is drawn at random. find the probability of its being either a Queen or a heart. 4/13
23) 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
24) A number is chosen from number 1 to 100. Find the probability of its being divisible by 4 or 6. 33/100
25) A die is thrown twice. What is the probability that at least one of the two throws comes up with the number 4 ? 11/36
26) Two dice are tossed once. find the probability of getting an even number on the first die or a total of eight. 5/9
27) two dice are thrown together. what is the probability that sum of the numbers on the two faces is neither divisible by 3 nor by 4 ? 4/9
28) In a class, 30% of the students offered mathematics, 20% offered chemistry and 10% offered both. if a student is selected at random. find the probability that he has offered mathematics or chemistry. 2/5
29) the probability that Ahmed passes and English is 2/3 and the probability that he passes in Hindi is 5/9. if the probability of his passing both the subjects is 2/5, find the probability that he will pass in at least 1 of the subjects. 37/45
30) the probability that a person will get an electrification contract is 2/5 and the probability that he will not get a plumbing contract is 4/7. if the probability of getting at least one contract is 2/3, what is the prob. that he will get both ? 17/105
31) The probability that a patient visiting a dentist will have a tooth extracted is 0.06, the probability that he will have a cavity filled is 0.2, and the probability that he will have a tooth extracted or a cavity filled is 0.23. what is the probability that he will have a tooth extracted as well as a cavity filled? 0.03
32) In a town of 6000 people, 1200 are over 50 years old and 2000 are females. it is known that 30% of the females are over 50 years. what is the probability that a randomly chosen individual from the town is either female or over 50 years ?
13/30
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