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Probability — BITSAT Mathematics PYQs

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

44 questionsMathematicsSolutions on every page
1

The probability of getting 10 in a single throw of three fair dice is

BITSAT 2024 Solution View → 2

In a binomial distribution, the mean is 4 and variance is 3 . Then, its mode is

BITSAT 2024 Solution View → 3

The probability that certain electronic component fails when first used is 0.10 . If it does not fail immediately, the probability that it lasts for one year is 0.99 . The probabil

BITSAT 2024 Solution View → 4

Given below is the distribution of a random variable X If = P (X 3) and = P (X 2) , then : =

BITSAT 2024 Solution View → 5

A book contains 1000 pages. A page is chosen at random. The probability that the sum of the digits of the marked number on the page is equal to 9 , is

BITSAT 2024 Solution View → 6

For two events A and B , if P ( A )= P ( A B )= 1 4 and P ( B A )= 1 2 , then which of the following is not true?

BITSAT 2024 Solution View → 7

If A and B are mutually exclusive events and if P ( B )= 1 3 , P ( A B )= 13 21 , then P ( A ) is equal to

BITSAT 2023 Solution View → 8

A coin is tossed twice. Then, the probability that atleast one tail occurs is

BITSAT 2023 Solution View → 9

If E and F are events such that 0 < P ( F ) < 1 , then

BITSAT 2023 Solution View → 10

The probability of getting sum more than 7 when a pair of dice are thrown is:

BITSAT 2023 Solution View → 11

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

BITSAT 2023 Solution View → 12

Bag P contains 6 red and 4 blue balls and bag Q contains 5 red and 6 blue balls. A ball is transferred from bag P to bag Q and then a ball is drawn from bag Q . What is the probabi

BITSAT 2023 Solution View → 13

If P ( B )= 3 5 , P ( A B )= 1 2 and P ( A B )= 4 5 , then P ( A B )^ + P ( A ^ B )=

BITSAT 2023 Solution View → 14

A six faced die is a biased one. It is thrice more likely to show an odd numbers than show an even number. It is thrown twice. The probability that the sum of the numbers in two th

BITSAT 2022 Solution View → 15

Girl students constitute 10 % of I year and 5 % of II year at Roorkee University. During summer holidays 70 % of the I year and 30 % of II year students are given a project. The gi

BITSAT 2021 Solution View → 16

The mean and variance of a random variable X having binomial distribution are 4 and 2 respectively, then P ( X =1) is

BITSAT 2021 Solution View → 17

The probability that certain electronic component fails when first used is 0.10 . If it does not fail immediately, the probability that it lasts for one year is 0.99 . The probabil

BITSAT 2020 Solution View → 18

A die is thrown 7 times. What is the probability that an even number turns up at least 4 times?

BITSAT 2019 Solution View → 19

Three numbers are chosen at random without replacement from 1 , 2 , 3 , &#8230; &#8230; , 8 . The probability that their minimum is 3 , given that their maximum is 6 , is

BITSAT 2019 Solution View → 20

Cards are drawn one by one at random from a well shuffled pack of 52 cards until 2 aces are obtained for the first time. The probability that 18 draws are required for this is

BITSAT 2019 Solution View → 21

The sum of mean and variance of a Binomial distribution B D &#8594; for 3 trials is 2 . 7 , then the binomial distribution B D &#8594; is given by

BITSAT 2018 Solution View → 22

Let A and B are two independent events. If the probability that both A and B occur together is 1 6 and the probability that neither of them occurs is 1 3 , then the probability of

BITSAT 2018 Solution View → 23

In a test an examiner either guesses or copies or knows the answer to a multiple choice question with 4 choices. The probability that he/she makes a guess is 1 3 . The probability

BITSAT 2018 Solution View → 24

If the papers of 4 students can be checked by any one of the 7 teachers, then the probability that all the 4 papers are checked by exactly 2 teachers, is equal to

BITSAT 2017 Solution View → 25

A coin is tossed 7 times. Each time a man calls head. The probability that he wins the toss at least four times is

BITSAT 2017 Solution View → 26

A man takes a step forward with probability 0.4 and backward with probability 0.6 . The probability that at the end of eleven steps he is one step away from the starting point is

BITSAT 2016 Solution View → 27

A bag contains (2 n+1) coins. It is known that n of these coins have a head on both sides, whereas the remaining ( n +1) coins are fair. A coin is picked up at random from the bag

BITSAT 2015 Solution View → 28

A bag contains 3 red and 3 white balls. Two balls are drawn one by one. The probability that they are of different colours is.

BITSAT 2015 Solution View → 29

If in a binomial distribution n =4, P ( X =0)= 16 81 , then P ( X =4) equals

BITSAT 2015 Solution View → 30

A bag contains 5 brown and 4 white socks. A man pulls out 2 socks. Find the probability that they are of the same colour.

BITSAT 2014 Solution View → 31

A bag contains n+1 coins. It is known that one of these coins shows heads on both sides, whereas the other coins are fair. One coin is selected at random and tossed. If the probabi

BITSAT 2014 Solution View → 32

A coin is tossed 7 times. Each time a man calls head. Find the probability that he wins the toss on more occasions.

BITSAT 2014 Solution View → 33

For k=1,2,3 the box B _ k contains k red balls and (k+1) white balls. Let P ( B ₁ )= 1 2 , P ( B ₂ )= 1 3 and P ( B ₃ )= 1 6 . A box is selected at random and a ball is drawn from

BITSAT 2013 Solution View → 34

The probability of India winning a test match against West Indies is 1 / 2 . Assuming independence from match to match, the probability that in a 5 match series India's second win

BITSAT 2013 Solution View → 35

The probability of simultaneous occurrence of atleast one of two events A and B is p . If the probability that exactly one of A, B occurs is q then P (A^ )+P (B^ ) is equal to

BITSAT 2012 Solution View → 36

A boy is throwing stones at a target. The probability of hitting the target at any trial is 1 2 The probability of hitting the target 5 th time at the 10 th throw is:

BITSAT 2012 Solution View → 37

Two dice are thrown together 4 times. The probability that both dice will show same numbers twice is -

BITSAT 2012 Solution View → 38

If (A ) and ( B ) are mutually exclusive events and if ( P ( B )= 1 3 , P ( A B )= 13 21 ), then ( P ( A ) ) is equal to

BITSAT 2011 Solution View → 39

A die is loaded such that the probability of throwing the number (i ) is proportional to its reciprocal. The probability that 3 appears in a single throw is-

BITSAT 2011 Solution View → 40

If the mean, mode and S.D. of a frequency distribution are 41, 45 and 8 respectively, then its Pearson's coefficient of skewness is

BITSAT 2010 Solution View → 41

The equation of the plane containing the line ( x - x ₁ = y - y ₁ ~m = z - z ₁ n ) is (a (x-x₁ )+b (y-y₁ )+c (z-z₁ )=0 ), then

BITSAT 2010 Solution View → 42

If mean of a poisson distribution of a random variable (X ) is 2 , then the value of (P(X > 1.5) ) is

BITSAT 2010 Solution View → 43

A line segment has length 63 and direction ratios are (3,-2,6 ). If the line makes an obtuse angle with ( x )-axis, the components of the line vector are

BITSAT 2009 Solution View → 44

It is given that the events (A ) and (B ) are such that (P(A)= 1 4 , P(A B)= 1 2 ) and ( P(B A)= 2 3 ). Then (P(B) ) is

BITSAT 2009 Solution View →
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