Probability MCQ Questions & Answers

Probability MCQs : This section focuses on the "Probability". These Multiple Choice Questions (MCQs) should be practiced to improve the Probability skills required for various interviews (campus interview, walk-in interview, company interview), placement, entrance exam and other competitive examinations.

Question 1

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

A. 1/2

B. 2/5

C. 8/15

D. 9/20

Question 2

A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

A. 10/11

B. 11/21

C. 2/7

D. 5/7

Question 3

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

A. 1/3

B. 3/4

C. 7/19

D. 8/21

Question 4

What is the probability of getting a sum 9 from two throws of a dice?

A. 1/6

B. 1/8

C. 1/9

D. 1/12

Question 5

Three unbiased coins are tossed. What is the probability of getting at most two heads?

A. 3/4

B. 1/4

C. 3/8

D. 7/8

Question 6

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

A. 1/2

B. 3/4

C. 3/8

D. 5/16

Question 7

In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:

A. 21/42

B. 25/117

C. 1/50

D. 3/25

Question 8

In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

A. 1/10

B. 2/5

C. 2/7

D. 5/7

Question 9

From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?

A. 1/15

B. 25/57

C. 35/256

D. 1/221

Question 10

Two dice are tossed. The probability that the total score is a prime number is:

A. 1/6

B. 5/12

C. 1/2

D. 7/9

Question 11

A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:

A. 1/13

B. 2/13

C. 1/26

D. 1/52

Question 12

A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:

A. 1/22

B. 3/22

C. 2/91

D. 2/77

Question 13

Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:

A. 3/20

B. 29/34

C. 47/100

D. 13/102

Question 14

One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?

A. 1/13

B. 3/13

C. 1/4

D. 9/52

Question 15

A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?

A. 3/4

B. 4/7

C. 1/8

D. 3/7

Question 16

14 persons are seated around a circular table. Find the probability that 3 particular persons always seated together.

A. 11/379

B. 21/628

C. 24/625

D. 26/247

Question 17

8 couples (husband and wife) attend a dance show "Nach Baliye' in a popular TV channel ; A lucky draw in which 4 persons picked up for a prize is held, then the probability that there is atleast one couple will be selected is :

A. 8/39

B. 15/39

C. 12/13

D. None of these

Question 18

A bag contains 2 red Roses, 4 yellow Roses and 6 pink Roses. Two roses are drawn at random. What is the probability that they are not of same color?

A. 1/6

B. 2/3

C. 14/33

D. 5/6

Question 19

A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

A. 10/21

B. 11/21

C. 1/2

D. 2/7

Question 20

A bag contains 3 black, 4 white and 5 red balls. One ball is drawn at random. Find the probability that it is either black or red ball:

A. 2/3

B. 1/4

C. 5/12

D. 1/2

Question 21

A bag contains 3 red balls, 5 yellow balls and 7 pink balls. If one ball is drawn at random from the bag, what is the probability that it is either pink or red?

A. 2/3

B. 1/8

C. 3/8

D. 3/4

Question 22

A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is red.

A. 23/42

B. 19/42

C. 7/32

D. 16/39

Question 23

A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:

A. 2/91

B. 1/22

C. 3/22

D. 2/77

Question 24

A bag contains 5 red smileys, 6 yellow smileys and 3 green smileys. If two smileys are picked at random, what is the probability that both are red or both are green in colour?

A. 7

B. 1/7

C. 3/7

D. 0

Question 25

A bag contains 50 tickets numbered 1,2,3,4......50 of which five are drawn at random and arranged in ascending order of magnitude.Find the probability that third drawn ticket is equal to 30.

A. 551/15134

B. 1/2

C. 552/15379

D. 1/9

Question 26

A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?

A. 3/7

B. 4/7

C. 1/8

D. 3/4

Question 27

A bag contains 6 white and 4 black balls .2 balls are drawn at random. Find the probability that they are of same colour.

A. 1/2

B. 7/15

C. 8/15

D. 1/9

Question 28

A bag contains 7 green and 5 black balls. Three balls are drawn one after the other. The probability of all three balls being green, if the balls drawn are not replaced will be:

A. 123/897

B. 23/67

C. 7/44

D. 12/45

Question 29

A bag contains 8 red and 4 green balls. Find the probability that two balls are red and one ball is green when three balls are drawn at random.

A. 56/99

B. 112/495

C. 78/495

D. None of these

Question 30

A basket contains 10 apples and 20 oranges out of which 3 apples and 5 oranges are defective. If we choose two fruits at random, what is the probability that either both are oranges or both are non defective?

A. 136/345

B. 17/87

C. 316/435

D. 158/435

Question 31

A box contains 10 bulbs,of which just three are defective. If a random sample of five bulbs is drawn, find the probability that the sample contains exactly one defective bulb.

A. 5/12

B. 7/12

C. 3/14

D. 1/12

Question 32

A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?

A. 1/6

B. 1/3

C. 1/2

D. 1/4

Question 33

A box contains 5 detective and 15 non-detective bulbs. Two bulbs are chosen at random. Find the probability that both the bulbs are non-defective.

A. 5/19

B. 3/20

C. 21/38

D. None of these

Question 34

A brother and a sister appear for an interview against two vacant posts in an office. The probability of the brother’s selection is 1/5 and that of the sister’s selection is 1/3. What is the probability that only one of them is selected?

A. 1/5

B. 3/4

C. 2/5

D. 3/5

Question 35

A card is drawn from a pack of 52 cards. The card is drawn at random. What is the probability that it is neither a spade nor a Jack?

A. 9/13

B. 4/13

C. 10/13

D. 8/13

Question 36

A card is drawn from a pack of 52 cards. The probability of getting a queen of the club or a king of the heart is?

A. 1/26

B. 1/13

C. 2/13

D. 1/52

Question 37

A coin is tossed 5 times. What is the probability that head appears an odd number of times?

A. 1/2

B. 1/3

C. 2/3

D. 1

Question 38

A coin is tossed twice if the coin shows head it is tossed again but if it shows a tail then a die is tossed. If 8 possible outcomes are equally likely. Find the probability that the die shows a number greater than 4, if it is known that the first throw of the coin results in a tail

A. 1/3

B. 2/3

C. 2/5

D. 4/15

Question 39

A fair coin is tossed 11 times. What is the probability that only the first two tosses will yield heads ?

A. (1/2)^11

B. (9)(1/2)

C. (11C2)(1/2)^9

D. (1/2)

Question 40

A fair six-sided die is rolled twice. What is the probability of getting 4 on the first roll and not getting 6 on the second roll ?

A. 1/36

B. 5/36

C. 1/12

D. 1/9

Question 41

A five digit number is formed with the digits 0,1,2,3 and 4 without repetition. Find the chance that the number is divisible by 5.

A. 3/5

B. 1/5

C. 2/5

D. 4/5

Question 42

A group of five persons is formed from five boys and four girls. Find the probability that there are at least two girls in the group?

A. 110/129

B. 5/6

C. 121/126

D. 3/7

Question 43

A letter is takenout at random from 'ASSISTANT' and another is taken out from 'STATISTICS'. The probability that they are the same letter is :

A. 35/96

B. 19/90

C. 19/96

D. None of these

Question 44

A man and his wife appear in an interview for two vacancies in the same post. The probability of husband's selection is (1/7) and the probability of wife's selection is (1/5). What is the probability that only one of them is selected ?

A. 2/7

B. 1/7

C. 3/4

D. 4/5

Question 45

A number is selected at random from the numbers 1 to 30. What is the probability that it is divisible by either 3 or 7 ?

A. 1/30

B. 2/30

C. 1/25

D. 1/2

Question 46

A number is selected from the numbers 1,2,3,4.......25.The probability for it to be divisible by 4 or 7 is:

A. 3/25

B. 9/25

C. 1/25

D. None of these

Question 47

A number X is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3. What is the probability that |X|<2

A. 3/7

B. 3/4

C. 4/5

D. 5/7

Question 48

A person starting with 64 rupees and making 6 bets, wins three times and loses three times, the wins and loses occurring in random order. The chance for a win is equal to the chance for a loss. If each wager is for half the money remaining at the time of the bet, then the final result is:

A. A gain of Rs. 27

B. A loss of Rs. 37

C. A loss of Rs. 27

D. A gain of Rs. 37

Question 49

A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?

A. 1/4

B. 1/2

C. 3/4

D. 7/12

Question 50

A room contains 3 brown, 5 black and 4 white chairs. Two chairs are picked and are put in the lawn. What is the probability that none of the chairs picked is white ?

A. 14/33

B. 14/55

C. 12/55

D. 13/33

Question 51

A six-sided die with faces numbered 1 through 6 is rolled three times. What is the probability that the face with the number 6 on it will not face upward on all the three rolls?

A. 215/216

B. 1/216

C. 215/256

D. 1/52

Question 52

A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident

A. 30/100

B. 35/100

C. 45/100

D. 50/100

Question 53

A table tennis player, lost 12 games out of 18 games played. Calculate the games won in terms of decimal.

A. 0.667

B. 0.067

C. 0.5

D. 0.333

Question 54

A three-digit number is formed with the digits 1, 2, 3, 4, 5 at random. What is probability that number formed is divisible by 5 ?

A. 1/4

B. 1/5

C. 1/2

D. 3/4

Question 55

Ajay and his wife Reshmi appear in an interview for two vaccancies in the same post. The Probability of Ajay's selection is 1/7 and that of his wife Reshmi's selection is 1/5. What is the probability that only one of them will be selected?

A. 5/7

B. 1/5

C. 2/7

D. 2/35

Question 56

An unbiased cubic die is thrown.What is the probabiltiy of getting a multiple of 3 or 4?

A. 1/12

B. 1/9

C. 3/4

D. 1/2

Question 57

An unbiased die is rolled. Find the probability of getting a multiple of 3?

A. 1/6

B. 1/3

C. 5/6

D. None of these

Question 58

An unbiased die is tossed.Find the probability of getting a multiple of 3.

A. 1/3

B. 1/2

C. 3/4

D. 3/2

Question 59

An urn contains 4 white 6 black and 8 red balls . If 3 balls are drawn one by one without replacement, find the probability of getting all white balls.

A. 5/204

B. 1/204

C. 13/204

D. None of these

Question 60

fifteen persons are sitting around a circular table facing the centre. What is the probability that three particular persons sit together ?

A. 3/91

B. 2/73

C. 1/91

D. 3/73

Question 61

Find the median, mode and mean of 9, 5, 8, 9, 9, 7, 8, 9, 8.

A. 9, 9, 9

B. 9, 8, 9

C. 8, 9, 8

D. 8, 9, 9

Question 62

Find the probability of selecting 2 woman when four persons are choosen at random from a group of 3 men, 2 woman and 4 children.

A. 1/5

B. 1/7

C. 1/6

D. 1/9

Question 63

Find the probability of selecting exactly 2 children when four persons are choosen at random from a group of 3 men, 2 woman and 4 children.

A. 9/29

B. 10/21

C. 12/21

D. 14/19

Question 64

Find the probability that it is either white or red ball when,one ball is drawn at random in a bag that contains 3 black,4 white and 5 red balls

A. 0.5

B. 0.75

C. 0.25

D. 0.8

Question 65

Find the probability that one ball is white when two balls are drawn at random from a basket that contains 9 red, 7 white and 4 black balls.

A. 18/95

B. 18/190

C. 1/2

D. 91/190

Question 66

Find the range and mode of the data 17, 18, 28, 19, 16, 18, 17, 29, 18

A. 12 and 18

B. 13 and 18

C. 12 and 17

D. 11 and 17

Question 67

Find the range of the data 2, 1, 2, 3, 5, 4, 7, 3, 5, 2, 4.

A. 5

B. 4

C. 3

D. 6

Question 68

Find the standard deviation of {11, 7, 10,13, 9}

A. 1

B. 2

C. 4

D. 5

Question 69

Four dice are thrown simultaneously. Find the probability that all of them show the same face.

A. 1/216

B. 1/36

C. 2/216

D. 4/216

Question 70

Four dice are thrown simultaneously. Find the probability that two of them show the same face and remaining two show the different faces.

A. 4/9

B. 5/9

C. 11/18

D. 7/9

Question 71

Four persons are to be choosen from a group of 3 men, 2 women and 4 children. Find the probability of selecting 1 man,1 woman and 2 children.

A. 2/7

B. 3/7

C. 4/7

D. 3/7

Question 72

From a pack of 52 cards, 3 cards are drawn. What is the probability that one is ace, one is queen and one is jack?

A. 19/5525

B. 16/5525

C. 17/5525

D. 7/5525

Question 73

From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?

A. 1/15

B. 1/221

C. 25/57

D. 35/256

Question 74

From well shuffled standard pack of 52 playing cards,one card is drawn. What is the probability that it is either a red card or black card?

A. 1/2

B. 3/4

C. 1

D. 1/3

Question 75

I forgot the last digit of a 7-digit telephone number. If 1 randomly dial the final 3 digits after correctly dialing the first four, then what is the chance of dialing the correct number?

A. 1/999

B. 1/1001

C. 1/1000

D. 4/1000

Question 76

If a box contains 10 bulbs,of which just three are defective. If a random sample of five bulbs is drawn, find the probability that the sample contains no defective bulbs.

A. 5/12

B. 7/12

C. 3/14

D. 1/12

Question 77

If a card is drawn at random from a pack of 52 cards,what is the chance of getting a spade or ace?

A. 0.25

B. 5/13

C. 0.2

D. 4/13

Question 78

If an unbiased dice is rolled once, the odds in favour of getting a point which is multiple of 3 is:

A. 1/2

B. 2/1

C. 1/3

D. 3/1

Question 79

If p:q are the odds in favour of an event,then the probability of that event is:

A. p/q

B. p/(p+q)

C. q/(p+q)

D. none

Question 80

If the difference between the mode and median is 2, then the difference between the median and mean is:

A. 2

B. 1

C. 3

D. 4

Question 81

If the standard deviation of a population is 10, what would be the population variance?

A. 100

B. 30

C. 5

D. 20

Question 82

If the standard deviation of a population is 4.5, what would be the population variance?

A. 20.25

B. 20

C. 9

D. 18

Question 83

If the standard deviation of a population is 6.5, what would be the population variance?

A. 40.25

B. 42.25

C. 18.25

D. 13

Question 84

If the standard deviation of a population is 7, what would be the population variance?

A. 14

B. 21

C. 49

D. 28

Question 85

If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is ?

A. 1

B. 1/2

C. 0

D. 3/5

Question 86

If two letters are taken at random from the word HOME, what is the probability that none of the letters would be vowels?

A. 1/6

B. 1/2

C. 1/3

D. 1/4

Question 87

If x is chosen at random from the set {1,2,3,4} and y is to be chosen at random from the set {5,6,7}, what is the probability that xy will be even?

A. 1/2

B. 2/3

C. 3/4

D. 4/3

Question 88

Consider 5 independent Bernoulli’s trials each with probability of success p. If the probability of at least one failure is greater than or equal to 31/32 , then p lies in the interval ?

A. [1, 32]

B. (0, 1)

C. [1, 1/2]

D. (1, 1/2]

Question 89

In a bag which contains 40 balls, there are 18 red balls and some green and blue balls. If two balls are picked up from the bag without replacement, then the probability of the first ball being red and second being green is 3/26. Find the number of blue balls in the bag.

A. 16

B. 12

C. 10

D. 14

Question 90

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

A. 1/3

B. 3/5

C. 8/21

D. 7/21

Question 91

In a box, there are 9 blue, 6 white and some black stones. A stone is randomly selected and the probability that the stone is black is ¼. Find the total number of stones in the box?

A. 15

B. 18

C. 20

D. 24

Question 92

In a box, there are four marbles of white color and five marbles of black color. Two marbles are chosen randomly. What is the probability that both are of the same color?

A. 2/9

B. 5/9

C. 4/9

D. 0

Question 93

In a charity show tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random (blindly) will have a number with a hundredth digit of 2?

A. 0.25

B. 0.5

C. 0.75

D. 0.4

Question 94

In a class, 30% of the students offered English, 20% offered Hindi and 10% offered both. If a student is selected at random, what is the probability that he. has offered English or Hindi ?

A. 1/2

B. 3/4

C. 4/5

D. 2/5

Question 95

In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:

A. 21/46

B. 1/5

C. 3/25

D. 1/50

Question 96

In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize ?

A. 1/7

B. 2/7

C. 3/7

D. 2/5

Question 97

In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

A. 2/7

B. 5/7

C. 1/5

D. 1/2

Question 98

In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples ?

A. 6/7

B. 19/21

C. 7/31

D. 5/21

Question 99

In a purse there are 30 coins, twenty one-rupee and remaining 50-paise coins. Eleven coins are picked simultaneously at random and are placed in a box. If a coin is now picked from the box, find the probability of it being a rupee coin?

A. 4/7

B. 2/3

C. 1/2

D. 5/6

Question 100

In a race, the odd favour of cars P,Q,R,S are 1:3, 1:4, 1:5 and 1:6 respectively. Find the probability that one of them wins the race.

A. 319/420

B. 27/111

C. 114/121

D. 231/420

Question 101

In a simultaneous throw of pair of dice. Find the probability of getting the total more than 7.

A. 1/2

B. 5/12

C. 7/15

D. 3/12

Question 102

In a simultaneous throw of two dice, what is the probability of getting a doublet ?

A. 1/6

B. 1/3

C. 4/7

D. 4/5

Question 103

In a simultaneous throw of two dice, what is the probability of getting a total of 7 ?

A. 1/6

B. 1/4

C. 1/20

D. 3/4

Question 104

In a single throw of two dice , find the probability that neither a doublet nor a total of 8 will appear.

A. 7/15

B. 5/18

C. 13/18

D. 3/16

Question 105

In a single throw with 2 dices, what is probability of neither getting an even number on one and nor a multiple of 3 on other?

A. 11/36

B. 25/36

C. 5/6

D. 1/6

Question 106

In a throw of a coin, find the probability of getting a head.

A. 1

B. 1/2

C. 1/4

D. 0.1

Question 107

One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?

A. 3/13

B. 1/13

C. 3/52

D. 9/52

Question 108

One card is drawn from a pack of 52 cards , each of the 52 cards being equally likely to be drawn. Find the probability that the card drawn is neither a spade nor a king.

A. 0

B. 9/13

C. 1/2

D. 4/13

Question 109

One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn find the probability the card drawn is red.

A. 2/3

B. 1/2

C. 1/52

D. 13/51

Question 110

One card is drawn from a pack of 52 cards,each of the 52 cards being equally likely to be drawn.Find the probability that the ball drawn is an ace :

A. 1/13

B. 1/12

C. 1/14

D. 1/15

Question 111

One card is drawn from deck of 52 cards, each of the 52 cards being equally likely to be drawn. Find the probability that the ball drawn is red.

A. 1/3

B. 1/2

C. 1/4

D. 1/6

Question 112

One lady has 2 children, one of her child is boy, what is the probability of having both are boys ?

A. 1/3

B. 1/2

C. 2/3

D. 2/5

Question 113

Out of 17 applicants 8 boys and 9 girls. Two persons are to be selected for the job. Find the probability that at least one of the selected persons will be a girl.

A. 19/34

B. 5/4

C. 20/34

D. 25/34

Question 114

Out of 3 girls and 6 boys a group of three members is to be formed in such a way that at least one member is a girl. In how many different ways can it be done?

A. 64

B. 84

C. 56

D. 20

Question 115

Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is ?

A. 16/19

B. 1

C. 3/2

D. 17/20

Question 116

Out of sixty students, there are 14 who are taking Economics and 29 who are taking Calculus. What is the probability that a randomly chosen student from this group is taking only the Calculus class ?

A. 8/15

B. 7/15

C. 1/15

D. 4/15

Question 117

The first 8 alphabets are written down at random. what is the probability that the letters b,c,d,e always come together ?

A. 1/7

B. 8!

C. 7!

D. 1/14

Question 118

The letters of the word CASTIGATION is arranged in different ways randomly. What is the chance that vowels occupy the even places ?

A. 0.04

B. 0.043

C. 0.047

D. 0.05

Question 119

The Manager of a company accepts only one employees leave request for a particular day. If five employees namely Roshan, Mahesh, Sripad, Laxmipriya and Shreyan applied for the leave on the occasion of Diwali. What is the probability that Laxmi priya’s leave request will be approved ?

A. 1

B. 1/5

C. 5

D. 4/5

Question 120

The mean of 20 observations is 19. One more observation is included and the new mean becomes 20. The 21st observation is

A. 20

B. 30

C. 40

D. 42

Question 121

The mean of a distribution is 15 and the standard deviation is 5. What is the value of the coefficient variation?

A. 16.66%

B. 66.66%

C. 33.33%

D. 100%

Question 122

The mean of a distribution is 18 and the standard deviation is 4.5. What is the value of the coefficient of variation?

A. 50%

B. 25%

C. 100%

D. 75%

Question 123

The mean of a distribution is 20 and the standard deviation is 4. What is the value of the coefficient variation?

A. 10%

B. 20%

C. 40%

D. 60%

Question 124

The mean of distribution is 11 and the standard deviation is 5. What is the value of the coefficient variation?

A. 45.45%

B. 35.35%

C. 25.25%

D. 55.55%

Question 125

The mean of the data 2, 9, 9, 3, 6, 9, 4 is

A. 33/7

B. 6

C. 43/7

D. 7

Question 126

The odds favouring the event of a person hitting a target are 3 to 5. The odds against the event of another person hitting the target are 3 to 2. If each of them fire once at the target, find the probability that both of them hit the target.

A. 1/20

B. 4/20

C. 1/20

D. 3/20

Question 127

The probabilities that A and B will tell the truth are 2 / 3 and 4 / 5 respectively . What is the probability that they agree with each other ?

A. 3/5

B. 1/3

C. 2/5

D. 3/4

Question 128

The probabilities that a student will receive an A, B, C or D grade are 0.4, 0.3 , 0.2 and 0.1 respectively. Find the probability that a student will receive Atleast B grade.

A. 0.21

B. 0.3

C. 0.7

D. None of these

Question 129

The probabilities that drivers A, B and C will drive home safely after consuming liquor are 2 / 5, 3 / 7 and 3 / 4, respectively. What is the probability that they will drive home safely after consuming liquor ?

A. 3/70

B. 4/70

C. 9/70

D. 1/50

Question 130

The probability of occurance of two two events A and B are 1/4 and 1/2 respectively. The probability of their simultaneous occurrance is 7/50. Find the probability that neither A nor B occurs.

A. 25/99

B. 39/100

C. 61/100

D. 17/100

Question 131

The probability of success of three students X, Y and Z in the one examination are 1/5, 1/4 and 1/3 respectively. Find the probability of success of at least two.

A. 1/4

B. 1/2

C. 1/6

D. 1/3

Question 132

The probability that a bowler bowled a ball from a point will hit by the batsman is ¼. Three such balls are bowled simultaneously towards the batsman from that very point. What is the probability that the batsman will hit the ball ?

A. 37/64

B. 27/56

C. 11/13

D. 9/8

Question 133

The probability that a card drawn at random from the pack of playing cards may be either a queen or an ace is:

A. 9/13

B. 11/13

C. 2/13

D. None of these

Question 134

The probability that a card drawn from a pack of 52 cards will be a diamond or a king, is

A. 5/12

B. 4/13

C. 5/13

D. 3/14

Question 135

The probability that a number selected at random from the first 100 natural numbers is a composite number is ?

A. 3/2

B. 2/3

C. 1/2

D. 34/7

Question 136

The probability that z lies between 0 and 3.01

A. 0.4987

B. 0.5

C. 0.9987

D. 0.1217

Question 137

The probabiltiy that throw of two dice yields a total of 5 or 6 is:

A. 2/14

B. 5/18

C. 3/4

D. 1/4

Question 138

The standard deviation of the set {10, 11, 12, 9, 8} is

A. 1

B. √2

C. 2

D. 2√2

Question 139

The variance of a set of data is 121. Then the standard deviation of the data is

A. +-11

B. 11

C. 21

D. 60.5

Question 140

There are 10 Letters and 10 correspondingly 10 different Address. If the letter are put into envelope randomly, then find the Probability that Exactly 9 letters will at the Correct Address ?

A. 1/10

B. 1/9

C. 1

D. 0

Question 141

There are 26 balls marked with alphabetical order A to Z. What is the probability of selecting vowels listed balls?

A. 1

B. 21/26

C. 5/26

D. 5

Question 142

There are four hotels in a town. If 3 men check into the hotels in a day then what is the probability that each checks into a different hotel?

A. 1/2

B. 3/4

C. 4/7

D. 3/8

Question 143

Three dice are thrown together.Find the probability of getting a total of atleast 6.

A. 103/216

B. 103/108

C. 103/36

D. 36/103

Question 144

Three fair coins are tossed simultaneously. Find the probability of getting more heads than the number of tails

A. 2

B. 7/8

C. 5/8

D. 1/2

Question 145

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is :

A. 2/9

B. 1/9

C. 8/9

D. 7/9

Question 146

Three unbiased coins are tossed. What is the probability of getting at most two heads ?

A. 4/3

B. 2/3

C. 3/2

D. 3/4

Question 147

Three unbiased coins are tossed. What is the probability of getting at most two heads?

A. 3/4

B. 7/8

C. 1/2

D. 1/4

Question 148

Three unbiased coins are tossed.What is the probability of getting at least 2 heads?

A. 1/4

B. 1/2

C. 3/4

D. 1/3

Question 149

Tickets are numbered from 1 to 18 are mixed up together and then 9 tickets are drawn at random. Find the probability that the ticket has a number, which is a multiple of 2 or 3.

A. 1/3

B. 3/5

C. 2/3

D. 5/6

Question 150

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5 ?

A. 2/3

B. 1/2

C. 7/8

D. 4/5

Question 151

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

A. 1/2

B. 3/5

C. 9/20

D. 8/15

Question 152

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 4 or 15 ?

A. 6/19

B. 3/10

C. 7/10

D. 6/17

Question 153

Two brother X and Y appeared for an exam. The probability of selection of X is 1/7 and that of B is 2/9. Find the probability that both of them are selected.

A. 1/63

B. 1/14

C. 2/63

D. 1/9

Question 154

Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen?

A. 52/221

B. 55/190

C. 55/221

D. 19/221

Question 155

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 queens?

A. 17/112

B. 55/221

C. 55/121

D. 33/221

Question 156

Two cards are drawn from a pack of well shuffled cards. Find the probability that one is a club and other in King

A. 1/52

B. 1/26

C. 1/13

D. 1/2

Question 157

Two dice are rolled simultaneously. Find the probability of getting a total of 9.

A. 1/3

B. 1/9

C. 8/9

D. 9/10

Question 158

Two dice are rolled simultaneously. Find the probability of getting the sum of numbers on the on the two faces divisible by 3 or 4?

A. 3/7

B. 7/11

C. 5/9

D. 6/13

Question 159

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

A. 3/4

B. 3/8

C. 5/16

D. 2/7

Question 160

Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6.

A. 7/18

B. 14/35

C. 8/18

D. 7/35

Question 161

Two dice are tossed. The probability that the total score is a prime number is :

A. 1/6

B. 1/2

C. 5/12

D. 3/4

Question 162

Two dice are tossed. The probability that the total score is a prime number is:

A. 5/12

B. 1/6

C. 1/2

D. 7/9

Question 163

Two letters are randomly chosen from the word TIME. Find the probability that the letters are T and M?

A. 1/4

B. 1/6

C. 1/8

D. 4

Question 164

Two unbiased coin are tossed. What is the probability of getting atmost one head?

A. 1/2

B. 3/2

C. 1/6

D. 3/4

Question 165

What is the probability of an impossible event?

A. 0

B. -1

C. 0.1

D. 1

Question 166

What is the probability of getting 53 Mondays in a leap year?

A. 1/7

B. 3/7

C. 2/7

D. 1

Question 167

What is the probability of getting a sum 9 from two throws of a dice ?

A. 1/6

B. 1/2

C. 1/9

D. 3/4

Question 168

What is the probability of getting a sum 9 from two throws of a dice?

A. 1/2

B. 3/4

C. 1/9

D. 2/9

Question 169

What is the probability of getting at least one six in a single throw of three unbiased dice?

A. 1/36

B. 91/256

C. 13/256

D. 43/256

Question 170

What is the probability that a couple with four children have atleast one girl?

A. 0.0625

B. 0.9375

C. 0.5

D. 0.0257

Question 171

What is the probability that a leap year has 53 Saturdays and 52 Sundays ?

A. 1/7

B. 2/7

C. 1/2

D. 3/2

Question 172

What is the probability that a leap year selected at random, will contain 53 sundays?

A. 1/7

B. 1/3

C. 2/7

D. 4/7

Question 173

What is the probability that a number is divisible by 4?

A. 2

B. 1/2

C. 1/4

D. 1

Question 174

What is the probability that it is either a heart card or diamond card, when a card is drawn from a well shuffled standard pack of 52 playing cards?

A. 1

B. 1/2

C. 3/4

D. 1/3

Question 175

What is the probabiltiy of getting a mutliple of 2 or 5 when an unbiased cubic die is thrown?

A. 1/3

B. 1/2

C. 2/3

D. 1/6

Question 176

When two dice are thrown simultaneously, what is the probability that the sum of the two numbers that turn up is less than 12?

A. 35/36

B. 17/36

C. 15/36

D. 1/36

Question 177

Which of the following questions is a statistical question?

A. Where do the professional sports leagues play?

B. How many professional sports leagues are there?

C. How many hours do the student-athletes at your school spend each week training for a sports league?

D. How many hours of professional training took place over the weekend?

Question 178

X attempts 94 questions and gets 141 marks. If for every correct answer 4 marks is given, and for every wrong answer 1 mark is deducted, then the number of questions wrongly answered by X is __.

A. 45

B. 47

C. 57

D. 40

Question 179

You toss a coin AND roll a die. What is the probability of getting a tail and a 4 on the die?

A. 1/2

B. 1/12

C. 2/3

D. 3/4

Question 180

A speaks truth in 60% cases B speaks truth in 70% cases. The probability that they will way say the same thing while describing a single event, is-

A. 0.54

B. 0.56

C. 0.68

D. 0.94

Question 181

A speaks truth in 75% cases and B in 80% of the cases. In what percentage of cases are they likely to contradict each other, in narrating the same incident ?

A. 5%

B. 15%

C. 35%

D. 45%

Question 182

Which of the following is not an example of a discrete probability distribution?

A. The number of bathrooms in a house

B. The sale or purchase price of a house

C. The number of bedrooms in a house

D. Whether or not a home has a swimming pool in it

Question 183

The collection of one or more outcomes from an experiment is called

A. Event

B. Z-Value

C. Probability

D. Random Variable

Question 184

The probability of success changes from trial to trial in

A. Sampling distribution

B. Binomial distribution

C. Hypergeometric distribution

D. Geometric distribution

Question 185

Successive trials in binomial distribution are

A. Dependent

B. Independent

C. Equally Likely

D. Mutually exclusive

Question 186

Each trial in Binomial distribution has

A. One Outcome

B. Two Outcome

C. Three Outcome

D. Four Outcome

Question 187

In a Poisson probability distribution

A. It always contains a contingency table

B. The number of trials is always less than 5

C. The probability of success is always greater than 5

D. The mean and variance of the distribution are same (equal)

Question 188

The the special rule of multiplication of probability, the events must be

A. Empirical

B. Bayesian

C. Independent

D. Independent

Question 189

A speaks truth in 75% cases and B in 80% of cases. In what percentage of cases they contradict each other in narrating the same incident?

A. 15%

B. 25%

C. 35%

D. 45%

Question 190

If the occurrence of one event means that another cannot happen, then the events are

A. Bayesian

B. Empirical

C. Independent

D. Mutually Exclusive

Question 191

A listing of the possible outcomes of an experiment and their corresponding probability is called

A. Bayesian table

B. Random Variable

C. Contingency table

D. Probability distribution

Question 192

Which of the following is not a correct statement about a probability.

A. A value near 0 means that the event is not likely to occur/happens

B. It can be reported as a decimal or a fraction

C. It must have a value between 0 and 1

D. It is the collection of several experiments

Question 193

In special rule of addition of probability, the events are always

A. Bayesian

B. Empirical

C. Independent events

D. Mutually Exclusive events

Question 194

Binomial distribution has parameters

A. 1

B. 2

C. 3

D. 4

Question 195

The variance of binomial distribution is always

A. Less than mean

B. Equal to mean

C. Greater than mean

D. Equal to standard deviation

Question 196

In which approach to probability the outcomes are equally likely to occur?

A. Classical Probability

B. Subjective Probability

C. Relative Frequency

D. Independent

Question 197

Which of the following is not a condition of the binomial distribution?

A. trials must be independent

B. must have at least 3 trials

C. only 2 possible outcomes

D. have constant probability of success

Question 198

The successive trials are with replacement in

A. Geometric distribution

B. Binomial distribution

C. Hypergeometric distribution

D. None of above

Question 199

The mean, median and mode for binomial distribution will be equal when

A. p = 0.5

B. p < 0.5

C. p > 0.5

D. p = 1

Question 200

Hypergeometric distribution has parameters

A. 1

B. 2

C. 3

D. 4

Question 201

Which of the following is not the property of binomial distribution

A. N is fixed

B. Has two outcomes

C. Trials are independent

D. Probability of success varies from trial to trial

Question 202

The distribution function F(X) is represented by

A. P(X)

B. P(X = x)

C. P(X > x)

D. P(X ≤ x)

Question 203

The probability function is always

A. Negative

B. Non Negative

C. Positive

D. None of these

Question 204

Binomial distribution is symmetrical when

A. p = q

B. p > q

C. p < q

D. np > npq

Question 205

Probability of occurrence of an event lies between

A. 0 and 1

B. -1 and 0

C. -1 and 1

D. exactly 1

Question 206

A discrete probability distribution may be represented by

A. A table

B. A graph

C. A mathematical Equation

D. All of these

Question 207

In which distribution successive trials are without replacement

A. Poisson distribution

B. Binomial distribution

C. Geometric distribution

D. Hypergeometric distribution

Question 208

In hypergeometric distribution, the trials are

A. Dependent

B. Independent

C. Collectively Exhaustive

D. None of these

Question 209

For a random variable X, E(X) is

A. Harmonic Mean (HM)

B. Geometric Mean (GM)

C. Arithmetic Mean (AM)

D. None of these

Question 210

Two teams Arrogant and Overconfident are participating in a cricket tournament. The odds that team Arrogant will be champion is 5 to 3, and the odds that team Overconfident will be the champion is 1 to 4. What are the odds that either Arrogant or team Overconfident will become the champion?

A. 3 to 2

B. 5 to 2

C. 6 to 1

D. 33 to 7

Question 211

A speaks truth in 75% of cases and B in 80% of cases. In what percent of cases are they likely to contradict each other in narrating the same event?

A. 35%

B. 5%

C. 45%

D. 22.50%

Question 212

The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on at least one ticket is -

A. 0.4869

B. 0.5904

C. 0.6234

D. 0.5834

Question 213

Three unbiased coins are tossed. What is the probability of getting at least 2 tails?

A. 0.75

B. 0.5

C. 0.25

D. 0.2