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Probability — NDA Mathematics PYQs

201 previous year questions from Probability with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

201 questionsMathematicsSolutions on every page
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Passage: Four dice are rolled. Question: What is the probability that getting a total of the numbers on the dice is 6 ?

NDA 2026 Solution View → 2

Three events A , B and C are such that A and B are disjoint, A and C are independent, B and C are independent. If 4P(A)=2P(B)=P(C) and P(A B C)=5P(A) , then what is the value of P(

NDA 2026 Solution View → 3

Passage: Let A , B , C and D be mutually exclusive and exhaustive events and P(A) 2 = P(B) 3 = P(C) 5 = P(D) 8 . Question: What is [2P(A)+3P(B)] [4P(C)+5P(D)] equal to ?

NDA 2026 Solution View → 4

Passage: Four dice are rolled. Question: What is the probability that getting a total of the numbers on the dice is at least 23 ?

NDA 2026 Solution View → 5

For a Binomial distribution with mean 6 and standard deviation 2 , what is the value of P(X=0) ?

NDA 2026 Solution View → 6

Passage: A 4-digit number is selected at random formed by using the digits 0 , 1 , 2 , 3 and 4 (where repetition of digits is not allowed). Question: What is the probability that t

NDA 2026 Solution View → 7

In an entrance test there are multiple choice questions. There are four options for each question, of which only one is correct. The probability that a student knows the answer to

NDA 2026 Solution View → 8

Passage: Let A , B , C and D be mutually exclusive and exhaustive events and P(A) 2 = P(B) 3 = P(C) 5 = P(D) 8 . Question: If G is the geometric mean of P(A) , P(B) , P(C) and P(D)

NDA 2026 Solution View → 9

Consider the following statements in respect of the events A , B , C : I. (A B C) ( A B C ) is an impossible event. II. (A B C) ( A B C ) is a possible event. Which of the statemen

NDA 2026 Solution View → 10

Passage: Let A , B , C and D be mutually exclusive and exhaustive events and P(A) 2 = P(B) 3 = P(C) 5 = P(D) 8 . Question: What is P(A)+P(B)+P(C) equal to ?

NDA 2026 Solution View → 11

The probability that a family owns a laptop is 0.68 ; that it also owns a desktop is 0.56 . If the probability that it owns both is 0.48 , then what is the probability that a rando

NDA 2025 Solution View → 12

An urn contains 10 white and 5 red balls. If two balls are drawn at random, then what is the probability that both the balls are red?

NDA 2025 Solution View → 13

An urn contains 5 white, 6 red and 4 blue balls. Three balls are drawn at random. What is the probability that a white ball, a red ball and a blue ball are drawn?

NDA 2025 Solution View → 14

Under which of the following conditions may binomial distribution be used? I. The number of trials is infinite and not fixed. II. The trials are independent. III. Each trial has tw

NDA 2025 Solution View → 15

Three faces of a die are black, two faces are white and one face is red. The die is tossed three times. What is the probability that the colours black, white and red appear in the

NDA 2025 Solution View → 16

A person X speaks the truth 4 out of 5 times and person Y speaks the truth 5 out of 6 times. What is the probability that they will contradict each other in stating the fact?

NDA 2025 Solution View → 17

An event X can happen with probability p and event Y can happen with probability q . Further, X and Y are independent events. Which of the following statements is/are correct? I. T

NDA 2025 Solution View → 18

A fair coin is tossed 4 times. What is the probability that two heads do not occur consecutively?

NDA 2025 Solution View → 19

In a throw of three dice, what is the probability of getting one prime number, one composite number and one number which is neither prime nor composite?

NDA 2025 Solution View → 20

If P(A) = 0.3 , P(B) = 0.4 and P(A|B) = 0.5 , then what is the value of P(B|A) ?

NDA 2025 Solution View → 21

Out of 50 consecutive natural numbers, two integers are chosen at random. What is the probability that their sum is odd?

NDA 2025 Solution View → 22

If P(A) = 1/3 , P(B) = 1/2 and P(A B) = 1/4 , then what is the value of P( A B) ?

NDA 2025 Solution View → 23

Consider the following for the two (02) items that follow: Let X be a random variable following binomial distribution with parameters n = 6 and p = k . Further, 9P(X = 4) = P(X = 2

NDA 2025 Solution View → 24

Consider the following for the two (02) items that follow: Let X be a random variable following binomial distribution with parameters n = 6 and p = k . Further, 9P(X = 4) = P(X = 2

NDA 2025 Solution View → 25

In a sample survey of a village, the probability that a farmer is in debt is 0.60 . What is the probability that three randomly selected farmers are all in debt (assume independenc

NDA 2025 Solution View → 26

Consider the following for the two (02) items that follow: A committee of 6 members is formed from a group of 7 gentlemen and 4 ladies. What is the probability that the committee i

NDA 2025 Solution View → 27

Consider the following for the two (02) items that follow: A committee of 6 members is formed from a group of 7 gentlemen and 4 ladies. What is the probability that the committee i

NDA 2025 Solution View → 28

Consider the following for the two (02) items that follow: The probabilities that A , B and C become managers are 3 10 , 1 2 and 4 5 respectively. The probabilities that bonus sche

NDA 2025 Solution View → 29

If P(A) = 1 3 , P(B) = 1 2 and P(A B) = 1 4 , then what is the value of P(A^c B^c) ?

NDA 2025 Solution View → 30

Consider the following for the two (02) items that follow: The probabilities that A , B and C become managers are 3 10 , 1 2 and 4 5 respectively. The probabilities that bonus sche

NDA 2025 Solution View → 31

If two fair dice are tossed, then what is the probability that the sum of the numbers on the faces of the dice is strictly greater than 7?

NDA 2025 Solution View → 32

The probability of a man hitting a target is 1 5 . If the man fires 7 times, then what is the probability that he hits the target at least twice?

NDA 2025 Solution View → 33

Let X be a random variable following binomial distribution whose mean and variance are 200 and 160 respectively. What is the value of the number of trials (n) ?

NDA 2025 Solution View → 34

The probability that a student passes Physics test is 2/3 and the probability that he passes both Physics test and English test is 11/15 . The probability that he passes at least o

NDA 2025 Solution View → 35

An integer is chosen at random from the first 50 integers. What is the probability that the integer is neither divisible by 5 nor 9?

NDA 2025 Solution View → 36

If P(A) = 1 3 , P(B) = 1 2 and P(A B) = 1 4 , then what is the value of P(B | A^c) ?

NDA 2025 Solution View → 37

Let X be a random variable following binomial distribution with parameters n = 5 and p = k . Further, P(X = 1) = 0.4096 and P(X = 2) = 0.2048 . What is the value of k ?

NDA 2025 Solution View → 38

Three distinct natural numbers are chosen at random from 1 to 10 . What is the probability that they are consecutive?

NDA 2024 Solution View → 39

A die has two faces with number 4 , three faces with number 5 and one face with number 6 . If the die is rolled once, then what is the probability of getting 4 or 5 ?

NDA 2024 Solution View → 40

A , B , C are three mutually exclusive and exhaustive events associated with a random experiment. If 3 P ( B )=4 P ( A ) and 3 P ( C )=2 P ( B ) , then what is P ( A ) equal to?

NDA 2024 Solution View → 41

A can hit a target 5 times in 6 shots, B can hit 4 times in 5 shots and C can hit 3 times in 4 shots. What is the probability that A and C may hit but B may lose?

NDA 2024 Solution View → 42

A box contains 2 black, 4 yellow and 6 white balls. Three balls are drawn in succession with replacement. What is the probability that all three are of the same colour?

NDA 2024 Solution View → 43

For two events A and B , P ( A )= P ( A B )=0.25 and P ( B A )=0.5 . Which of the following are correct? A. A and B are independent. B. P ( A ^ C B ^ C )=0.875 C. P ( A ^ C B ^ C )

NDA 2024 Solution View → 44

A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6 ?

NDA 2024 Solution View → 45

Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is

NDA 2024 Solution View → 46

Two perfect dice are thrown. What is the probability that the sum of the numbers on the faces is neither 9 nor 10 ?

NDA 2024 Solution View → 47

Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?

NDA 2024 Solution View → 48

A natural number x is chosen at random from the first 100 natural numbers. What is the probability that x^2+x>50 ?

NDA 2024 Solution View → 49

The occurrence of a disease in an industry is such that the workers have 20 % chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more

NDA 2024 Solution View → 50

A bag contains 5 black and 4 white balls. A man selects two balls at random. What is the probability that both of these are of the same colour?

NDA 2024 Solution View → 51

If a random variable (x) follows binomial distribution with mean 5 and variance 4 , and 5 ²³ P ( X =3)= 4^ , then what is the value of ?

NDA 2024 Solution View → 52

If two random variable X and Y are connected by relation 2 X -3 Y 5 X +4 Y =4 and X follows Binomial distribution with parameters n=10 and p= 1 2 , then what is the variance of Y ?

NDA 2024 Solution View → 53

A , B , and C are three events such that P ( A )=0.6 , P ( B )=0.4, P ( C )=0.5, P ( A B )=0.8, P ( A C )=0.3 and P ( A B C )=0.2 and P ( A B C ) 0.85 . What is the minimum value o

NDA 2024 Solution View → 54

In a binomial distribution, if the mean is 6 and the standard deviation is 2 , then what are the values of the parameters n and p respectively?

NDA 2024 Solution View → 55

An unbiased coin is tossed n times. The probability of getting at least one tail is p and the probability of at What is the value of p+q ?

NDA 2024 Solution View → 56

An unbiased coin is tossed n times. The probability of getting at least one tail is p and the probability of at What is the value of n ?

NDA 2024 Solution View → 57

Three different numbers are selected at random from the first 15 natural numbers. What is the probability that the product of two of the numbers is equal to third number?

NDA 2024 Solution View → 58

A , B , and C are three events such that P ( A )=0.6 , P ( B )=0.4, P ( C )=0.5, P ( A B )=0.8, P ( A C )=0.3 and P ( A B C )=0.2 and P ( A B C ) 0.85 . What is the maximum value o

NDA 2024 Solution View → 59

Let A and B be two events such that P ( A B ) 0.75 and 0.125 P ( A B ) 0.375 . What is the maximum value of P ( A )+ P ( B ) ?

NDA 2024 Solution View → 60

If the letters of the word "TIRUPATI" are written down at random, then what is the probability that both Ts are always consecutive?

NDA 2024 Solution View → 61

Let A and B be two events such that P ( A B ) 0.75 and 0.125 P ( A B ) 0.375 . What is the minimum value of P ( A )+ P ( B ) ?

NDA 2024 Solution View → 62

Three dice are thrown. What is the probability of getting a sum which is a perfect square?

NDA 2023 Solution View → 63

Two distinct natural numbers from 1 to 9 are picked at random. What is the probability that their product has 1 in its unit place?

NDA 2023 Solution View → 64

The probability that a person recovers from a disease is 0.8. What is the probability that exactly 2 persons out of 5 will recover from the disease?

NDA 2023 Solution View → 65

Suppose that there is a chance for a newly constructed building to collapse, whether the design is faulty or not. The chance that the design is faulty is 10 % . The chance that the

NDA 2023 Solution View → 66

A fair coin is tossed 6 times. What is the probability of getting a result in the 6th toss which is different from those obtained in the first five tosses?

NDA 2023 Solution View → 67

In a class, there are n students including the students P and Q. What is the probability that P and Q sit together if seats are assigned randomly?

NDA 2023 Solution View → 68

In a Binomial distribution B(n, p), n=6 and 9 P(X=4)= P ( X =2) . What is p equal to?

NDA 2023 Solution View → 69

Three boys, P, Q, R an three girls S, T, U are to be arranged in a row for a group photograph. What is the probability that boys and girls sit alternatively?

NDA 2023 Solution View → 70

Three boys, P, Q, R an three girls S, T, U are to be arranged in a row for a group photograph. What is the probability that P and Q take the two end positions?

NDA 2023 Solution View → 71

Three boys, P, Q, R an three girls S, T, U are to be arranged in a row for a group photograph. What is the probability that Q and U sit together?

NDA 2023 Solution View → 72

A biased coin with the probability of getting head equal to 1 4 is tossed five times. What is the probability of getting tail in all the first four tosses followed by head?

NDA 2023 Solution View → 73

Let A and B be two independent events such that P( A )=0.7, P( B )=k, P(A B)=0.8 What is the value of k ?

NDA 2023 Solution View → 74

A coin is biased so that heads comes up thrice as likely as tails. In four independent tossess of the coin, what is probability of getting exactly three heads?

NDA 2023 Solution View → 75

Let X and Y be two random variables such that X + Y =100 . If X follows Binomial distribution with parameters n=100 and p= 4 6 , what is the variance of Y ?

NDA 2023 Solution View → 76

A, B. C and D are mutually exclusive and exhaustive events. If 2 P ( A )=3 P (B)=4 P ( C )=5 P ( D ) , then what is 77 P ( A ) equal to?

NDA 2023 Solution View → 77

Three dice are thrown. What is the probability that each face shows only multiples of 3 ?

NDA 2023 Solution View → 78

Two dice are thrown. What is the probability that difference of number on them is 2 or 3 ?

NDA 2023 Solution View → 79

What is the probability that the month of December has 5 Sundays ?

NDA 2023 Solution View → 80

One bag contains 3 white and 2 black balls, another bag contains 2 white and 3 black balls. Two balls are drawn from the first bag and put it into the second bag and then a ball is

NDA 2023 Solution View → 81

A natural number n is chosen from the first 50 natural numbers. What is the probability that n+ 50 n 50 ?

NDA 2023 Solution View → 82

Three fair dice are tossed once. What is the probability that they show different numbers that are in A P ?

NDA 2022 Solution View → 83

A number x is chosen at random from first n natural numbers. What is the probability that the number chosen satisfies x+ 1 x 2 ?

NDA 2022 Solution View → 84

What is the probability of getting a composite number in the list of natural numbers from 1 to 50 ?

NDA 2022 Solution View → 85

If P(A)=0.5, P(B)=0.7 and P(A B)=0 3 , then what is the value of P (A^ B^ )+P (A^ B )+P (A B^ ) ?

NDA 2022 Solution View → 86

A card is drawn from a pack of 52 cards. A gambler bets that it is either a spade or an ace. The odds against his winning are

NDA 2022 Solution View → 87

Five coins are tossed once. What is the probability of getting at most four tails?

NDA 2022 Solution View → 88

There are 90 applicants for a job. Some of them are graduates. Some of them have less than three years experience. array |c|c|c| & array c Number of graduates array & array c Numbe

NDA 2022 Solution View → 89

The completion of a construction job may be delayed due to strike. The probability of strike is 0.6 . The probability that the construction job gets completed on time if there is n

NDA 2022 Solution View → 90

Two digits out of 1,2,3,4,5 are chosen at random and multiplied together. What is the probability that the last digit in the product appears as 0 ?

NDA 2022 Solution View → 91

There are 90 applicants for a job. Some of them are graduates. Some of them have less than three years experience. array |c|c|c| & array c Number of graduates array & array c Numbe

NDA 2022 Solution View → 92

There are 90 applicants for a job. Some of them are graduates. Some of them have less than three years experience. array |c|c|c| & array c Number of graduates array & array c Numbe

NDA 2022 Solution View → 93

The incidence of suffering from a disease among workers in an industry has a chance of 33 1 3 % . What is the probability that exactly 3 out of 6 workers suffer from a disease?

NDA 2022 Solution View → 94

The incidence of suffering from a disease among workers in an industry has a chance of 33 1 3 % . What is the probability that no one out of 6 workers suffers from a disease?

NDA 2022 Solution View → 95

The incidence of suffering from a disease among workers in an industry has a chance of 33 1 3 % . What is the probability that at least one out of 6 workers suffer from a disease?

NDA 2022 Solution View → 96

Two numbers x and y are chosen at random from a set of first 10 natural numbers. What is the probability that (x+y) is divisible by 4 ?

NDA 2022 Solution View → 97

Three fair dice are thrown. What is the probability of getting a total greater than or equal to 15 ?

NDA 2022 Solution View → 98

During war one ship out of 5 was sunk on an average in making a certain voyage. What is the probability that exactly 3 out of 5 ships would arrive safely?

NDA 2022 Solution View → 99

The probability that a person hits a target is 0 5 . What is the probability of at least one hit in 4 shots?

NDA 2022 Solution View → 100

Consider the following relations for two events E and F : array ll 1. & P(E F) P(E)+P(F)-1 2. & P(E F)=P(E)+P(F)+P(E F) 3. & P(E F) P(E)+P(F) array Which of the above relations is/

NDA 2021 Solution View → 101

If P(A B) P(A) , then which one of the following is correct?

NDA 2021 Solution View → 102

In a cricket match, a batsman hits a six 8 times out of 60 balls he plays. What is the probability that on a ball played he does not hit a six?

NDA 2021 Solution View → 103

A problem is given to three students A, B and C , whose probabilities of solving the problem independently are 1 2 , 3 4 and p respectively. If the probability that the problem can

NDA 2021 Solution View → 104

3-digit numbers are formed using the digits 1,3,7 without repetition of digits. A number is randomly selected. What is the probability that the number is divisible by 3 ?

NDA 2021 Solution View → 105

If A and B are two events such that P( not A)= 7 10 , P( not B)= 3 10 and P(A B)= 3 14 , then what is P(B A) equal to?

NDA 2021 Solution View → 106

Let two events A and B be such that P(A)=L and P(B)=M . Which one of the following is correct?

NDA 2021 Solution View → 107

If P(A B)= 5 6 , P(A B)= 1 3 and P( A )= 1 2 , then which of the following is/are correct? 1. A and B are independent events. 2. A and B are mutually exclusive events. Select the c

NDA 2021 Solution View → 108

If A and B are two events such that P(A)= 3 4 and P(B)= 5 8 , then consider the following statements : 1. The minimum value of P(A B) is 3 4 . 2. The maximum value of P(A B) is 5 8

NDA 2021 Solution View → 109

In a binomial distribution, the mean is 2 3 and variance is 5 9 . What is the probability that random variable X=2 ?

NDA 2021 Solution View → 110

A coin is tossed twice. If E and F denote occurrence of head on first toss and second toss respectively, then what is P(E F) equal to?

NDA 2021 Solution View → 111

What is the probability that February of a leap year selected at random, will have five Sundays?

NDA 2020 Solution View → 112

A dealer has a stock of 15 gold coins out of which 6 are counterfeits. A person randomly picks 4 of the 15 gold coins. What is the probability that all the coins picked will be cou

NDA 2020 Solution View → 113

A husband and wife appear in an interview for two vacancies for the same post. The probability of the husband's selection is 1 7 and that of wife's selection is 1 5 . If the events

NDA 2020 Solution View → 114

A committee of 3 is to be formed from a group of 2 boys and 2 girls. What is the probability that the committee consists of 2 boys and 1 girl?

NDA 2020 Solution View → 115

Three cooks X, Y and Z bake a special kind of cake, and with respective probabilities 0.02,0.03 and 0.05 , it fails to rise. In the restaurant where they work, X bakes 50 %, Y bake

NDA 2020 Solution View → 116

If A and B are two events such that P(A)=0.6, P(B)=0.5 and P(A B)=0.4 , then consider the following statements : 1. P( A B)=0.9 . 2. P( B A )=0.6 . Which of the above statements is

NDA 2020 Solution View → 117

Consider a random variable X which follows Binomial distribution with parameters n=10 and p= 1 5 . Then Y=10-X follows Binomial distribution with parameters n and p respectively gi

NDA 2020 Solution View → 118

If three dice are rolled under the condition that no two dice show the same face, then what is the probability that one of the faces is having the number 6 ?

NDA 2020 Solution View → 119

In a lottery of 10 tickets numbered 1 to 10 , two tickets are drawn simultaneously. What is the probability that both the tickets drawn have prime numbers?

NDA 2020 Solution View → 120

If P(A B)= 5 6 , P(A B)= 1 3 and P( not A)= 1 2 , then which one of the following is not correct?

NDA 2020 Solution View →
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