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JEE Main

Probability

Mathematics

Previous Years Questions

MCQ (Single Correct Answer)

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Five numbers x1, x2, x3, x4, x5 are selected randomly from set {1, 2, 3, ....., 18} such that x1 2 3 4 5, then the proba...
JEE Main 2022 (Online) 27th June Morning Shift [ Memory Based ]
A blased coin is tossed 5 times and probability of getting exactly 4 heads is equal to probability of getting exactly 5 ...
JEE Main 2022 (Online) 26th June Morning Shift [ Memory Based ]
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JEE Main 2022 (Online) 24th June Evening Shift [ Memory Based ]
For a binomial probability distribution (33, p) such that 3P(X = 0) = P(X = 1) then find $${{P(X = 15)} \over {P(X = 18)...
JEE Main 2022 (Online) 24th June Morning Shift [ Memory Based ]
Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is :...
JEE Main 2021 (Online) 1st September Evening Shift
Let S = {1, 2, 3, 4, 5, 6}. Then the probability that a randomly chosen onto function g from S to S satisfies g(3) = 2g(...
JEE Main 2021 (Online) 31st August Evening Shift
Each of the persons A and B independently tosses three fair coins. The probability that both of them get the same number...
JEE Main 2021 (Online) 27th August Evening Shift
When a certain biased die is rolled, a particular face occurs with probability $${1 \over 6} - x$$ and its opposite face...
JEE Main 2021 (Online) 27th August Morning Shift
Two fair dice are thrown. The numbers on them are taken as $$\lambda$$ and $$\mu$$, and a system of linear equationsx + ...
JEE Main 2021 (Online) 26th August Evening Shift
A fair die is tossed until six is obtained on it. Let x be the number of required tosses, then the conditional probabili...
JEE Main 2021 (Online) 26th August Evening Shift
Let A and B be independent events such that P(A) = p, P(B) = 2p. The largest value of p, for which P (exactly one of A, ...
JEE Main 2021 (Online) 26th August Morning Shift
The probability that a randomly selected 2-digit number belongs to the set {n $$\in$$ N : (2n $$-$$ 2) is a multiple of ...
JEE Main 2021 (Online) 27th July Morning Shift
Let X be a random variable such that the probability function of a distribution is given by $$P(X = 0) = {1 \over 2},P(X...
JEE Main 2021 (Online) 25th July Evening Shift
A student appeared in an examination consisting of 8 true-false type questions. The student guesses the answers with equ...
JEE Main 2021 (Online) 27th July Evening Shift
Let 9 distinct balls be distributed among 4 boxes, B1, B2, B3 and B4. If the probability than B3 contains exactly 3 ball...
JEE Main 2021 (Online) 25th July Morning Shift
Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 $$\times$$ 2 matrices. The pro...
JEE Main 2021 (Online) 22th July Evening Shift
Let A, B and C be three events such that the probability that exactly one of A and B occurs is (1 $$-$$ k), the probabil...
JEE Main 2021 (Online) 20th July Evening Shift
The probability of selecting integers a$$\in$$[$$-$$ 5, 30] such that x2 + 2(a + 4)x $$-$$ 5a + 64 > 0, for all x$$\i...
JEE Main 2021 (Online) 20th July Morning Shift
Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the l...
JEE Main 2021 (Online) 20th July Morning Shift
Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096...
JEE Main 2021 (Online) 18th March Evening Shift
Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrenc...
JEE Main 2021 (Online) 17th March Evening Shift
Two dies are rolled. If both dices have six faces numbered 1, 2, 3, 5, 7 and 11, then the probability that the sum of th...
JEE Main 2021 (Online) 17th March Morning Shift
Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3. Then...
JEE Main 2021 (Online) 16th March Evening Shift
A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the ...
JEE Main 2021 (Online) 16th March Morning Shift
A seven digit number is formed using digits 3, 3, 4, 4, 4, 5, 5. The probability, that number so formed is divisible by ...
JEE Main 2021 (Online) 26th February Evening Shift
A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to probability of getting ...
JEE Main 2021 (Online) 26th February Morning Shift
In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are n...
JEE Main 2021 (Online) 25th February Evening Shift
Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen ...
JEE Main 2021 (Online) 25th February Evening Shift
The coefficients a, b and c of the quadratic equation, ax2 + bx + c = 0 are obtained by throwing a dice three times. The...
JEE Main 2021 (Online) 25th February Morning Slot
When a missile is fired from a ship, the probability that it is intercepted is $${1 \over 3}$$ and the probability that ...
JEE Main 2021 (Online) 25th February Morning Slot
The probability that two randomly selected subsets of the set {1, 2, 3, 4, 5} have exactly two elements in their interse...
JEE Main 2021 (Online) 24th February Evening Slot
An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal t...
JEE Main 2021 (Online) 24th February Morning Slot
The probabilities of three events A, B and C are given by P(A) = 0.6, P(B) = 0.4 and P(C) = 0.5. If P(A$$ \cup $$B) = 0....
JEE Main 2020 (Online) 6th September Evening Slot
Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability...
JEE Main 2020 (Online) 6th September Morning Slot
In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on t...
JEE Main 2020 (Online) 4th September Evening Slot
The probability that a randomly chosen 5-digit number is made from exactly two digits is :
JEE Main 2020 (Online) 3rd September Evening Slot
A dice is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4. Then the co...
JEE Main 2020 (Online) 3rd September Morning Slot
Let EC denote the complement of an event E. Let E1 , E2 and E3 be any pairwise independent events with P(E1) > 0 a...
JEE Main 2020 (Online) 2nd September Evening Slot
Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and...
JEE Main 2020 (Online) 2nd September Morning Slot
If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes conta...
JEE Main 2020 (Online) 9th January Evening Slot
A random variable X has the following probability distribution : .tg {border-collapse:collapse;border-spacing:0;width:...
JEE Main 2020 (Online) 9th January Evening Slot
In a box, there are 20 cards, out of which 10 are lebelled as A and the remaining 10 are labelled as B. Cards are drawn ...
JEE Main 2020 (Online) 9th January Morning Slot
Let A and B be two events such that the probability that exactly one of them occurs is $${2 \over 5}$$ and the probabili...
JEE Main 2020 (Online) 8th January Evening Slot
Let A and B be two independent events such that P(A) = $${1 \over 3}$$ and P(B) = $${1 \over 6}$$. Then, which of the fo...
JEE Main 2020 (Online) 8th January Morning Slot
In a workshop, there are five machines and the probability of any one of them to be out of service on a day is $${{1 \ov...
JEE Main 2020 (Online) 7th January Evening Slot
An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value of k when k consecutive heads are ob...
JEE Main 2020 (Online) 7th January Morning Slot
For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the...
JEE Main 2019 (Online) 12th April Evening Slot
A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins Rs. 12 when th...
JEE Main 2019 (Online) 12th April Evening Slot
If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed wi...
JEE Main 2019 (Online) 12th April Morning Slot
Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99%...
JEE Main 2019 (Online) 10th April Evening Slot
Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the co...
JEE Main 2019 (Online) 10th April Morning Slot
Four persons can hit a target correctly with probabilities $${1 \over 2}$$, $${1 \over 3}$$, $${1 \over 4}$$ and $${1 \o...
JEE Main 2019 (Online) 9th April Morning Slot
The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at lea...
JEE Main 2019 (Online) 8th April Evening Slot
Let A and B be two non-null events such that A $$ \subset $$ B . Then, which of the following statements is always corre...
JEE Main 2019 (Online) 8th April Morning Slot
In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these student...
JEE Main 2019 (Online) 12th January Evening Slot
In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number o...
JEE Main 2019 (Online) 12th January Evening Slot
In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experi...
JEE Main 2019 (Online) 12th January Morning Slot
A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If...
JEE Main 2019 (Online) 11th January Evening Slot
Let  S = {1, 2, . . . . . ., 20}. A subset B of S is said to be "nice", if the sum of the elements of B is 20...
JEE Main 2019 (Online) 11th January Evening Slot
Two integers are selected at random from the set {1, 2, ...., 11}. Given that the sum of selected numbers is even, the c...
JEE Main 2019 (Online) 11th January Morning Slot
If the probability of hitting a target by a shooter, in any shot, is $${1 \over 3}$$, then the minimum number of indepen...
JEE Main 2019 (Online) 10th January Evening Slot
An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers o...
JEE Main 2019 (Online) 10th January Morning Slot
An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ...
JEE Main 2019 (Online) 9th January Evening Slot
Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variabl...
JEE Main 2019 (Online) 9th January Morning Slot
Two different families A and B are blessed with equal numbe of children. There are 3 tickets to be distributed amongst t...
JEE Main 2018 (Online) 16th April Morning Slot
Let A, B and C be three events, which are pair-wise independent and $$\overrightarrow E $$ denotes the completement of a...
JEE Main 2018 (Online) 16th April Morning Slot
A player X has a biased coin whose probability of showing heads is p and a player Y has a fair coin. They start playing ...
JEE Main 2018 (Online) 15th April Evening Slot
A box 'A' contains $$2$$ white, $$3$$ red and $$2$$ black balls. Another box 'B' contains $$4$$ white, $$2$$ red and $$3...
JEE Main 2018 (Online) 15th April Morning Slot
A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball alo...
JEE Main 2018 (Offline)
Let E and F be two independent events. The probability that both E and F happen is $${1 \over {12}}$$ and the probabilit...
JEE Main 2017 (Online) 9th April Morning Slot
From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woma...
JEE Main 2017 (Online) 9th April Morning Slot
An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :
JEE Main 2017 (Online) 8th April Morning Slot
Three persons P, Q and R independently try to hit a target. I the probabilities of their hitting the target are $${3 \ov...
JEE Main 2017 (Online) 8th April Morning Slot
A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the vari...
JEE Main 2017 (Offline)
If two different numbers are taken from the set {0, 1, 2, 3, ........, 10}; then the probability that their sum as well ...
JEE Main 2017 (Offline)
For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P (Exactly one of C or ...
JEE Main 2017 (Offline)
An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this exp...
JEE Main 2016 (Online) 10th April Morning Slot
If A and B are any two events such that P(A) = $${2 \over 5}$$ and P (A $$ \cap $$ B) = $${3 \over {20}}$$, hen the cond...
JEE Main 2016 (Online) 9th April Morning Slot
Let two fair six-faced dice $$A$$ and $$B$$ be thrown simultaneously. If $${E_1}$$ is the event that die $$A$$ shows up ...
JEE Main 2016 (Offline)
If $$12$$ different balls are to be placed in $$3$$ identical boxes, then the probability that one of the boxes contains...
JEE Main 2015 (Offline)
Let $$A$$ and $$B$$ be two events such that $$P\left( {\overline {A \cup B} } \right) = {1 \over 6},\,P\left( { {A \cap ...
JEE Main 2014 (Offline)
A multiple choice examination has $$5$$ questions. Each question has three alternative answers of which exactly one is c...
JEE Main 2013 (Offline)
Three numbers are chosen at random without replacement from $$\left\{ {1,2,3,..8} \right\}.$$ The probability that their...
AIEEE 2012
If $$C$$ and $$D$$ are two events such that $$C \subset D$$ and $$P\left( D \right) \ne 0,$$ then the correct statement ...
AIEEE 2011
Consider $$5$$ independent Bernoulli's trials each with probability of success $$p.$$ If the probability of at least one...
AIEEE 2011
An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random with...
AIEEE 2010
Four numbers are chosen at random (without replacement) from the set $$\left\{ {1,2,3,....20} \right\}.$$ Statement - 1...
AIEEE 2010
One ticket is selected at random from $$50$$ tickets numbered $$00, 01, 02, ...., 49.$$ Then the probability that the su...
AIEEE 2009
In a binomial distribution $$B\left( {n,p = {1 \over 4}} \right),$$ if the probability of at least one success is great...
AIEEE 2009
A die is thrown. Let $$A$$ be the event that the number obtained is greater than $$3.$$ Let $$B$$ be the event that the ...
AIEEE 2008
It is given that the events $$A$$ and $$B$$ are such that $$P\left( A \right) = {1 \over 4},P\left( {A|B} \right) = {1 ...
AIEEE 2008
A pair of fair dice is thrown independently three times. The probability of getting a score of exactly $$9$$ twice is
AIEEE 2007
Two aeroplanes $${\rm I}$$ and $${\rm I}$$$${\rm I}$$ bomb a target in succession. The probabilities of $${\rm I}$$ and ...
AIEEE 2007
At a telephone enquiry system the number of phone cells regarding relevant enquiry follow Poisson distribution with an a...
AIEEE 2006
Let $$A$$ and $$B$$ two events such that $$P\left( {\overline {A \cup B} } \right) = {1 \over 6},$$ $$P\left( {A \cap B}...
AIEEE 2005
A random variable $$X$$ has Poisson distribution with mean $$2$$. Then $$P\left( {X > 1.5} \right)$$ equals
AIEEE 2005
Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consult...
AIEEE 2005
The probability that $$A$$ speaks truth is $${4 \over 5},$$ while the probability for $$B$$ is $${3 \over 4}.$$ The pro...
AIEEE 2004
The mean and the variance of a binomial distribution are $$4$$ and $$2$$ respectively. Then the probability of $$2$$ suc...
AIEEE 2004
Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A select...
AIEEE 2003
The mean and variance of a random variable $$X$$ having binomial distribution are $$4$$ and $$2$$ respectively, then $$P...
AIEEE 2003
Events $$A, B, C$$ are mutually exclusive events such that $$P\left( A \right) = {{3x + 1} \over 3},$$ $$P\left( B \righ...
AIEEE 2003
A dice is tossed $$5$$ times. Getting an odd number is considered a success. Then the variance of distribution of succes...
AIEEE 2002
$$A$$ and $$B$$ are events such that $$P\left( {A \cup B} \right) = 3/4$$,$$P\left( {A \cap B} \right) = 1/4,$$ $$P\lef...
AIEEE 2002
A problem in mathematics is given to three students $$A,B,C$$ and their respective probability of solving the problem is...
AIEEE 2002

Numerical

More
If the probability that 6 digits number formed using digits 8 and 1 which is divisible by 21 is P then the value of 96 P...
JEE Main 2022 (Online) 26th June Evening Shift [ Memory Based ]
There are 10 questions in an exam, probability of correctly answering each of the first 4 questions is $${3 \over 4}$$ a...
JEE Main 2022 (Online) 24th June Evening Shift [ Memory Based ]
An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The p...
JEE Main 2021 (Online) 31st August Morning Shift
A fair coin is tossed n-times such that the probability of getting at least one head is at least 0.9. Then the minimum v...
JEE Main 2021 (Online) 25th July Evening Shift
Let there be three independent events E1, E2 and E3. The probability that only E1 occurs is $$\alpha$$, only E2 occurs i...
JEE Main 2021 (Online) 17th March Morning Shift
Let Bi (i = 1, 2, 3) be three independent events in a sample space. The probability that only B1 occur is $$\alpha $$, o...
JEE Main 2021 (Online) 24th February Morning Slot
In a bombing attack, there is 50% chance that a bomb will hit the target. Atleast two independent hits are required to d...
JEE Main 2020 (Online) 5th September Evening Slot
The probability of a man hitting a target is $${1 \over {10}}$$. The least number of shots required, so that the probabi...
JEE Main 2020 (Online) 4th September Morning Slot

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