# Probability · Mathematics · JEE Main

Start Practice## Numerical

JEE Main 2024 (Online) 9th April Morning Shift

Let $$\mathrm{a}, \mathrm{b}$$ and $$\mathrm{c}$$ denote the outcome of three independent rolls of a fair tetrahedral die, whose four faces are marked...

JEE Main 2024 (Online) 30th January Morning Shift

A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics and Chemistry. It was found that all students passed in atleast...

JEE Main 2024 (Online) 27th January Morning Shift

A fair die is tossed repeatedly until a six is obtained. Let $X$ denote the number of tosses required and let $a=P(X=3), b=P(X \geqslant 3)$ and $c=P(...

JEE Main 2023 (Online) 12th April Morning Shift

A fair $$n(n > 1)$$ faces die is rolled repeatedly until a number less than $$n$$ appears. If the mean of the number of tosses required is $$\frac{n}{...

JEE Main 2023 (Online) 11th April Evening Shift

Let the probability of getting head for a biased coin be $$\frac{1}{4}$$. It is tossed repeatedly until a head appears. Let $$\mathrm{N}$$ be the numb...

JEE Main 2023 (Online) 31st January Evening Shift

Let A be the event that the absolute difference between two randomly choosen real numbers in the sample space $[0,60]$ is less than or equal to a . If...

JEE Main 2023 (Online) 30th January Evening Shift

A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same...

JEE Main 2023 (Online) 25th January Evening Shift

25% of the population are smokers. A smoker has 27 times more chances to develop lung cancer than a non smoker. A person is diagnosed with lung cancer...

JEE Main 2023 (Online) 24th January Evening Shift

Three urns A, B and C contain 4 red, 6 black; 5 red, 5 black; and $$\lambda$$ red, 4 black balls respectively. One of the urns is selected at random a...

JEE Main 2022 (Online) 29th July Evening Shift

The sum and product of the mean and variance of a binomial distribution are 82.5 and 1350 respectively. Then the number of trials in the binomial dist...

JEE Main 2022 (Online) 28th July Evening Shift

A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let $$\mathrm{X}$$ be the number of white balls, among the dra...

JEE Main 2022 (Online) 30th June Morning Shift

The probability distribution of X is :
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JEE Main 2022 (Online) 27th June Evening Shift

Let S = {E1, E2, ........., E8} be a sample space of a random experiment such that $$P({E_n}) = {n \over {36}}$$ for every n = 1, 2, ........, 8. Then...

JEE Main 2022 (Online) 26th June Evening Shift

If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is p, then 96 p is equal to _________...

JEE Main 2022 (Online) 24th June Evening Shift

In an examination, there are 10 true-false type questions. Out of 10, a student can guess the answer of 4 questions correctly with probability $${3 \o...

JEE Main 2021 (Online) 1st September Evening Shift

Let X be a random variable with distribution.
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JEE Main 2021 (Online) 31st August Morning Shift

An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit...

JEE Main 2021 (Online) 27th August Evening Shift

The probability distribution of random variable X is given by :
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JEE Main 2021 (Online) 25th July Evening 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 value of n is ______________.

JEE Main 2021 (Online) 17th March Morning Shift

Let there be three independent events E1, E2 and E3. The probability that only E1 occurs is $$\alpha$$, only E2 occurs is $$\beta$$ and only E3 occurs...

JEE Main 2021 (Online) 24th February Morning Shift

Let Bi (i = 1, 2, 3) be three independent events in a sample space. The probability that only B1 occur is $$\alpha $$, only B2 occurs is $$\beta $$ an...

JEE Main 2020 (Online) 5th September Evening Slot

In a bombing attack, there is 50% chance that
a bomb will hit the target. Atleast two
independent hits are required to destroy the
target completely. ...

JEE Main 2020 (Online) 4th September Morning Slot

The probability of a man hitting a target is $${1 \over {10}}$$. The least number of shots required, so that the
probability of his hitting the target...

## MCQ (Single Correct Answer)

JEE Main 2024 (Online) 9th April Evening Shift

If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $$i^{\text {th }}$$ roll than the number obtained in the...

JEE Main 2024 (Online) 1st February Evening Shift

Let Ajay will not appear in JEE exam with probability $\mathrm{p}=\frac{2}{7}$, while both Ajay and Vijay will appear in the exam with probability $\m...

JEE Main 2024 (Online) 1st February Morning Shift

A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are whi...

JEE Main 2024 (Online) 31st January Evening Shift

A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and on...

JEE Main 2024 (Online) 31st January Morning Shift

Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable $$x$$ to be the number of rotten apples in a draw of t...

JEE Main 2024 (Online) 31st January Morning Shift

Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each draw...

JEE Main 2024 (Online) 30th January Evening Shift

Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probabilit...

JEE Main 2024 (Online) 30th January Morning Shift

Two integers $$x$$ and $$y$$ are chosen with replacement from the set $$\{0,1,2,3, \ldots, 10\}$$. Then the probability that $$|x-y|>5$$, is :

JEE Main 2024 (Online) 29th January Evening Shift

An integer is chosen at random from the integers $$1,2,3, \ldots, 50$$. The probability that the chosen integer is a multiple of atleast one of 4, 6 a...

JEE Main 2024 (Online) 29th January Morning Shift

A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is

JEE Main 2024 (Online) 27th January Evening Shift

An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that the first draw gives al...

JEE Main 2023 (Online) 15th April Morning Shift

A bag contains 6 white and 4 black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag ...

JEE Main 2023 (Online) 13th April Evening Shift

The random variable $$\mathrm{X}$$ follows binomial distribution $$\mathrm{B}(\mathrm{n}, \mathrm{p})$$, for which the difference of the mean and the ...

JEE Main 2023 (Online) 13th April Morning Shift

A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If $$\mathrm{X}$$ den...

JEE Main 2023 (Online) 12th April Morning Shift

Two dice A and B are rolled. Let the numbers obtained on A and B be $$\alpha$$ and $$\beta$$ respectively. If the variance of $$\alpha-\beta$$ is $$\...

JEE Main 2023 (Online) 11th April Morning Shift

Let $$S=\left\{M=\left[a_{i j}\right], a_{i j} \in\{0,1,2\}, 1 \leq i, j \leq 2\right\}$$ be a sample space and $$A=\{M \in S: M$$ is invertible $$\}$...

JEE Main 2023 (Online) 10th April Evening Shift

Let a die be rolled $$n$$ times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times...

JEE Main 2023 (Online) 10th April Morning Shift

Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that $${2^N} ...

JEE Main 2023 (Online) 8th April Evening Shift

If the probability that the random variable $$\mathrm{X}$$ takes values $$x$$ is given by $$\mathrm{P}(\mathrm{X}=x)=\mathrm{k}(x+1) 3^{-x}, x=0,1,2,3...

JEE Main 2023 (Online) 8th April Morning Shift

In a bolt factory, machines $$A, B$$ and $$C$$ manufacture respectively $$20 \%, 30 \%$$ and $$50 \%$$ of the total bolts. Of their output 3, 4 and 2 ...

JEE Main 2023 (Online) 6th April Evening Shift

Three dice are rolled. If the probability of getting different numbers on the three dice is $$\frac{p}{q}$$, where $$p$$ and $$q$$ are co-prime, then ...

JEE Main 2023 (Online) 6th April Morning Shift

A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If the probability of at least 4 successes is $$\frac{k}{3^{11...

JEE Main 2023 (Online) 1st February Evening Shift

Two dice are thrown independently. Let $$\mathrm{A}$$ be the event that the number appeared on the $$1^{\text {st }}$$ die is less than the number app...

JEE Main 2023 (Online) 1st February Morning Shift

In a binomial distribution $$B(n,p)$$, the sum and the product of the mean and the variance are 5 and 6 respectively, then $$6(n+p-q)$$ is equal to :...

JEE Main 2023 (Online) 31st January Morning Shift

A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black b...

JEE Main 2023 (Online) 30th January Morning Shift

If an unbiased die, marked with $$-2,-1,0,1,2,3$$ on its faces, is thrown five times, then the probability that the product of the outcomes is positiv...

JEE Main 2023 (Online) 29th January Evening Shift

Let $$\mathrm{S} = \{ {w_1},{w_2},......\} $$ be the sample space associated to a random experiment. Let $$P({w_n}) = {{P({w_{n - 1}})} \over 2},n \ge...

JEE Main 2023 (Online) 29th January Morning Shift

Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, ...

JEE Main 2023 (Online) 25th January Evening Shift

Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that $$N-2,\sqrt{3N},N+2$$ are in geometric progression...

JEE Main 2023 (Online) 25th January Morning Shift

Let M be the maximum value of the product of two positive integers when their sum is 66. Let the sample space $$S = \left\{ {x \in \mathbb{Z}:x(66 - x...

JEE Main 2023 (Online) 24th January Morning Shift

Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations
$$x + y + z = 1$$
$$2x + \mathrm{N}y ...

JEE Main 2023 (Online) 24th January Morning Shift

Let $$\Omega$$ be the sample space and $$\mathrm{A \subseteq \Omega}$$ be an event.
Given below are two statements :
(S1) : If P(A) = 0, then A = $$\p...

JEE Main 2022 (Online) 29th July Evening Shift

Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and...

JEE Main 2022 (Online) 29th July Morning Shift

Let $$S=\{1,2,3, \ldots, 2022\}$$. Then the probability, that a randomly chosen number n from the set S such that $$\mathrm{HCF}\,(\mathrm{n}, 2022)=1...

JEE Main 2022 (Online) 28th July Evening Shift

Let $$\mathrm{A}$$ and $$\mathrm{B}$$ be two events such that $$P(B \mid A)=\frac{2}{5}, P(A \mid B)=\frac{1}{7}$$ and $$P(A \cap B)=\frac{1}{9} \cdot...

JEE Main 2022 (Online) 28th July Morning Shift

Out of $$60 \%$$ female and $$40 \%$$ male candidates appearing in an exam, $$60 \%$$ candidates qualify it. The number of females qualifying the exam...

JEE Main 2022 (Online) 27th July Evening Shift

Let X have a binomial distribution B(n, p) such that the sum and the product of the mean and variance of X are 24 and 128 respectively. If $$P(X>n-3)=...

JEE Main 2022 (Online) 27th July Evening Shift

A six faced die is biased such that
$$3 \times \mathrm{P}($$a prime number$$)\,=6 \times \mathrm{P}($$a composite number$$)\,=2 \times \mathrm{P}(1)$$...

JEE Main 2022 (Online) 27th July Morning Shift

Let $$S$$ be the sample space of all five digit numbers. It $$p$$ is the probability that a randomly selected number from $$S$$, is a multiple of 7 bu...

JEE Main 2022 (Online) 26th July Evening Shift

Let $$X$$ be a binomially distributed random variable with mean 4 and variance $$\frac{4}{3}$$. Then, $$54 \,P(X \leq 2)$$ is equal to :

JEE Main 2022 (Online) 26th July Morning Shift

The mean and variance of a binomial distribution are $$\alpha$$ and $$\frac{\alpha}{3}$$ respectively. If $$\mathrm{P}(X=1)=\frac{4}{243}$$, then $$\m...

JEE Main 2022 (Online) 26th July Morning Shift

Let $$\mathrm{E}_{1}, \mathrm{E}_{2}, \mathrm{E}_{3}$$ be three mutually exclusive events such that $$\mathrm{P}\left(\mathrm{E}_{1}\right)=\frac{2+3 ...

JEE Main 2022 (Online) 25th July Evening Shift

If $$A$$ and $$B$$ are two events such that $$P(A)=\frac{1}{3}, P(B)=\frac{1}{5}$$ and $$P(A \cup B)=\frac{1}{2}$$, then $$P\left(A \mid B^{\prime}\ri...

JEE Main 2022 (Online) 25th July Morning Shift

If the sum and the product of mean and variance of a binomial distribution are 24 and 128 respectively, then the probability of one or two successes i...

JEE Main 2022 (Online) 25th July Morning Shift

If the numbers appeared on the two throws of a fair six faced die are $$\alpha$$ and $$\beta$$, then the probability that $$x^{2}+\alpha x+\beta>0$$, ...

JEE Main 2022 (Online) 30th June Morning Shift

If a random variable X follows the Binomial distribution B(5, p) such that P(X = 0) = P(X = 1), then $${{P(X = 2)} \over {P(X = 3)}}$$ is equal to :...

JEE Main 2022 (Online) 29th June Evening Shift

The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to :

JEE Main 2022 (Online) 29th June Morning Shift

The probability that a randomly chosen 2 $$\times$$ 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to :

JEE Main 2022 (Online) 28th June Evening Shift

The probability that a randomly chosen one-one function from the set {a, b, c, d} to the set {1, 2, 3, 4, 5} satisfies f(a) + 2f(b) $$-$$ f(c) = f(d) ...

JEE Main 2022 (Online) 28th June Morning Shift

The probability, that in a randomly selected 3-digit number at least two digits are odd, is :

JEE Main 2022 (Online) 27th June Evening Shift

If a point A(x, y) lies in the region bounded by the y-axis, straight lines 2y + x = 6 and 5x $$-$$ 6y = 30, then the probability that y ...

JEE Main 2022 (Online) 27th June Morning Shift

Five numbers $${x_1},{x_2},{x_3},{x_4},{x_5}$$ are randomly selected from the numbers 1, 2, 3, ......., 18 and are arranged in the increasing order $$...

JEE Main 2022 (Online) 27th June Morning Shift

Let X be a random variable having binomial distribution B(7, p). If P(X = 3) = 5P(x = 4), then the sum of the mean and the variance of X is :

JEE Main 2022 (Online) 26th June Morning Shift

Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of get...

JEE Main 2022 (Online) 25th June Evening Shift

A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is $${1 \over n}$$. If the die ...

JEE Main 2022 (Online) 25th June Morning Shift

Let E1 and E2 be two events such that the conditional probabilities $$P({E_1}|{E_2}) = {1 \over 2}$$, $$P({E_2}|{E_1}) = {3 \over 4}$$ and $$P({E_1} \...

JEE Main 2022 (Online) 24th June Evening Shift

A random variable X has the following probability distribution :
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JEE Main 2022 (Online) 24th June Morning Shift

Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2 balls drawn fro...

JEE Main 2022 (Online) 24th June Morning Shift

If a random variable X follows the Binomial distribution B(33, p) such that $$3P(X = 0) = P(X = 1)$$, then the value of $${{P(X = 15)} \over {P(X = 18...

JEE Main 2021 (Online) 1st September Evening Shift

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) 31st August 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(1) is :

JEE Main 2021 (Online) 27th 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 of heads is :

JEE Main 2021 (Online) 27th August Morning Shift

When a certain biased die is rolled, a particular face occurs with probability $${1 \over 6} - x$$ and its opposite face occurs with probability $${1 ...

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 probability P(x $$\ge$$ 5 | x > 2) i...

JEE Main 2021 (Online) 26th August Evening Shift

Two fair dice are thrown. The numbers on them are taken as $$\lambda$$ and $$\mu$$, and a system of linear equationsx + y + z = 5x + 2y + 3z = $$\mu$$...

JEE Main 2021 (Online) 26th August Morning 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, B occurs) = $${5 \over 9}$$, i...

JEE Main 2021 (Online) 27th July Evening Shift

A student appeared in an examination consisting of 8 true-false type questions. The student guesses the answers with equal probability.
the smallest ...

JEE Main 2021 (Online) 27th July Morning Shift

The probability that a randomly selected 2-digit number belongs to the set {n $$\in$$ N : (2n $$-$$ 2) is a multiple of 3} is equal to :

JEE Main 2021 (Online) 25th July Evening 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 = j) = {1 \over {{3^j}}}(j = ...

JEE Main 2021 (Online) 25th July Morning Shift

Let 9 distinct balls be distributed among 4 boxes, B1, B2, B3 and B4. If the probability than B3 contains exactly 3 balls is $$k{\left( {{3 \over 4}} ...

JEE Main 2021 (Online) 22th July Evening Shift

Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 $$\times$$ 2 matrices. The probability that such formed matr...

JEE Main 2021 (Online) 20th 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 probability that exactly one of B and ...

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 letter M appears at the fourth ...

JEE Main 2021 (Online) 20th July Morning Shift

The probability of selecting integers a$$\in$$[$$-$$ 5, 30] such that x2 + 2(a + 4)x $$-$$ 5a + 64 > 0, for all x$$\in$$R, is :

JEE Main 2021 (Online) 18th March Evening Shift

Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then...

JEE Main 2021 (Online) 17th March Evening Shift

Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be $${1 ...

JEE Main 2021 (Online) 17th March Morning 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 the numbers on the top faces is ...

JEE Main 2021 (Online) 16th March Evening 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 probability of event A is equ...

JEE Main 2021 (Online) 16th March Morning Shift

A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, i...

JEE Main 2021 (Online) 26th February Evening 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 2, is :

JEE Main 2021 (Online) 26th February Morning Shift

A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to probability of getting 9 heads, then the probability ...

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 element of A leaves remainder ...

JEE Main 2021 (Online) 25th February Evening Shift

In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and vegetarian. The...

JEE Main 2021 (Online) 25th February Morning Shift

When a missile is fired from a ship, the probability that it is intercepted is $${1 \over 3}$$ and the probability that the missile hits the target, g...

JEE Main 2021 (Online) 25th February Morning Shift

The coefficients a, b and c of the quadratic equation, ax2 + bx + c = 0 are obtained by throwing a dice three times. The probability that this equatio...

JEE Main 2021 (Online) 24th February Evening Shift

The probability that two randomly selected subsets of the set {1, 2, 3, 4, 5} have exactly two elements in their intersection, is :

JEE Main 2021 (Online) 24th February Morning Shift

An ordinary dice is rolled for a certain number of times. If the probability of getting an odd
number 2 times is equal to the probability of getting a...

JEE Main 2020 (Online) 6th September Evening 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) = 0.8, P(A$$ \cap $$C) = 0.3, P(A$...

JEE Main 2020 (Online) 6th September Morning Slot

Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with po...

JEE Main 2020 (Online) 4th September Evening 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 the two dice, in each throw is ...

JEE Main 2020 (Online) 3rd 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 Morning 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 conditional probability
that the...

JEE Main 2020 (Online) 2nd September Evening Slot

Let EC denote the complement of an event E.
Let E1
, E2
and E3
be any pairwise independent
events with P(E1) > 0
and P(E1 $$ \cap $$ E2 $$ \cap ...

JEE Main 2020 (Online) 2nd September Morning 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 a card is drawn
from it. The ...

JEE Main 2020 (Online) 9th January Evening Slot

A random variable X has the following
probability distribution :
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JEE Main 2020 (Online) 9th January Evening Slot

If 10 different balls are to be placed in 4 distinct
boxes at random, then the probability that two
of these boxes contain exactly 2 and 3 balls is :

JEE Main 2020 (Online) 9th January Morning 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 at random, one
after the other...

JEE Main 2020 (Online) 8th January Evening Slot

Let A and B be two events such that the
probability that exactly one of them occurs is $${2 \over 5}$$ and the probability that A or B occurs is $${1 ...

JEE Main 2020 (Online) 8th January Morning 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 following is TRUE?

JEE Main 2020 (Online) 7th January Evening 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 $${{1 \over 4}}$$
. If the probability ...

JEE Main 2020 (Online) 7th January Morning Slot

An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value of k when k
consecutive heads are obtained for k = 3, 4, 5, otherw...

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 the throw results in the sum of ...

JEE Main 2019 (Online) 12th April Evening Slot

For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability
that the candidate solve any problem i...

JEE Main 2019 (Online) 12th April Morning Slot

Let a random variable X have a binomial distribution with mean 8 and variance 4. If $$P\left( {X \le 2} \right) = {k \over {{2^{16}}}}$$, then k
is eq...

JEE Main 2019 (Online) 12th April Morning Slot

If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle
formed with these chosen vertices is eq...

JEE Main 2019 (Online) 10th April Evening 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% is :

JEE Main 2019 (Online) 10th April Morning 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 conditional probability that all...

JEE Main 2019 (Online) 9th April Morning Slot

Four persons can hit a target correctly with
probabilities
$${1 \over 2}$$, $${1 \over 3}$$, $${1 \over 4}$$ and
$${1 \over 8}$$ respectively. if all ...

JEE Main 2019 (Online) 8th April Evening 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 least 90% is :

JEE Main 2019 (Online) 8th April Morning Slot

Let A and B be two non-null events such that
A $$ \subset $$ B . Then, which of the following statements
is always correct?

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 on the die. If he decides to th...

JEE Main 2019 (Online) 12th January Evening 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 students is selected at random, then ...

JEE Main 2019 (Online) 12th January Morning Slot

In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth thr...

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 203. Then the probability that a...

JEE Main 2019 (Online) 11th January Evening 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 X be the number of white ball...

JEE Main 2019 (Online) 11th January Morning Slot

Two integers are selected at random from the set {1, 2, ...., 11}. Given that the sum of selected numbers is even, the conditional probability that bo...

JEE Main 2019 (Online) 10th January Evening Slot

If the probability of hitting a target by a shooter, in any shot, is $${1 \over 3}$$, then the minimum number of independent
shots at the target requi...

JEE Main 2019 (Online) 10th January Morning 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 obtained on them is noted. If t...

JEE Main 2019 (Online) 9th January Evening 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 ball is added to the urn and i...

JEE Main 2019 (Online) 9th January Morning Slot

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained i...

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 an event E. If $$P\left( {A \ca...

JEE Main 2018 (Online) 16th April Morning Slot

Two different families A and B are blessed with equal numbe of children. There are 3 tickets to be distributed amongst the children of these families ...

JEE Main 2018 (Offline)

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 along with two additional balls o...

JEE Main 2018 (Online) 15th April Evening 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 a game with their own coins an...

JEE Main 2018 (Online) 15th April Morning Slot

A box 'A' contains $$2$$ white, $$3$$ red and $$2$$ black balls. Another box 'B' contains $$4$$ white, $$2$$ red and $$3$$ black balls. If two balls a...

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 woman. Then the probability for th...

JEE Main 2017 (Online) 9th April Morning Slot

Let E and F be two independent events. The probability that both E and F happen is $${1 \over {12}}$$ and the probability that neither E nor F happens...

JEE Main 2017 (Online) 8th 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 $${3 \over 4},{1 \over 2}$$ and $${5 \...

JEE Main 2017 (Offline)

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with
replacement, then the variance of the number of green ba...

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 as absolute difference are bot...

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 A occurs) = $${1 \over 4}$$
a...

JEE Main 2016 (Online) 10th April Morning Slot

An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this experiment is :

JEE Main 2016 (Online) 9th 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 conditional probability, P(A $$\l...

JEE Main 2016 (Offline)

Let two fair six-faced dice $$A$$ and $$B$$ be thrown simultaneously. If $${E_1}$$ is the event that die $$A$$ shows up four, $${E_2}$$ is the event t...

JEE Main 2015 (Offline)

If $$12$$ different balls are to be placed in $$3$$ identical boxes, then the probability that one of the boxes contains exactly $$3$$ balls is :

JEE Main 2014 (Offline)

Let $$A$$ and $$B$$ be two events such that $$P\left( {\overline {A \cup B} } \right) = {1 \over 6},\,P\left( { {A \cap B} } \right) = {1 \over 4}$$ a...

JEE Main 2013 (Offline)

A multiple choice examination has $$5$$ questions. Each question has three alternative answers of which exactly one is correct. The probability that a...

AIEEE 2012

Three numbers are chosen at random without replacement from $$\left\{ {1,2,3,..8} \right\}.$$ The probability that their minimum is $$3,$$ given that ...

AIEEE 2011

Consider $$5$$ independent Bernoulli's trials each with probability of success $$p.$$ If the probability of at least one failure is greater than or eq...

AIEEE 2011

If $$C$$ and $$D$$ are two events such that $$C \subset D$$ and $$P\left( D \right) \ne 0,$$ then the correct statement among the following is :

AIEEE 2010

Four numbers are chosen at random (without replacement) from the set $$\left\{ {1,2,3,....20} \right\}.$$
Statement - 1: The probability that the cho...

AIEEE 2010

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. ...

AIEEE 2009

One ticket is selected at random from $$50$$ tickets numbered $$00, 01, 02, ...., 49.$$ Then the probability that the sum of the digits on the selecte...

AIEEE 2009

In a binomial distribution $$B\left( {n,p = {1 \over 4}} \right),$$ if the probability of at least one success is greater than or equal to $${9 \over...

AIEEE 2008

A die is thrown. Let $$A$$ be the event that the number obtained is greater than $$3.$$ Let $$B$$ be the event that the number obtained is less than $...

AIEEE 2008

It is given that the events $$A$$ and $$B$$ are such that
$$P\left( A \right) = {1 \over 4},P\left( {A|B} \right) = {1 \over 2}$$ and $$P\left( {B|A}...

AIEEE 2007

Two aeroplanes $${\rm I}$$ and $${\rm I}$$$${\rm I}$$ bomb a target in succession. The probabilities of $${\rm I}$$ and $${\rm I}$$$${\rm I}$$ scoring...

AIEEE 2007

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly $$9$$ twice is :

AIEEE 2006

At a telephone enquiry system the number of phone cells regarding relevant enquiry follow Poisson distribution with an average of $$5$$ phone calls du...

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 consulting others. The probability th...

AIEEE 2005

Let $$A$$ and $$B$$ two events such that $$P\left( {\overline {A \cup B} } \right) = {1 \over 6},$$ $$P\left( {A \cap B} \right) = {1 \over 4}$$ and $...

AIEEE 2004

The mean and the variance of a binomial distribution are $$4$$ and $$2$$ respectively. Then the probability of $$2$$ successes is :

AIEEE 2004

The probability that $$A$$ speaks truth is $${4 \over 5},$$ while the probability for $$B$$ is $${3 \over 4}.$$ The probability that they contradict ...

AIEEE 2003

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

AIEEE 2003

Events $$A, B, C$$ are mutually exclusive events such that $$P\left( A \right) = {{3x + 1} \over 3},$$ $$P\left( B \right) = {{1 - x} \over 4}$$ and $...

AIEEE 2003

Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is :

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\left( {\overline A } \right) = 2/...

AIEEE 2002

A dice is tossed $$5$$ times. Getting an odd number is considered a success. Then the variance of distribution of success is :

AIEEE 2002

A problem in mathematics is given to three students $$A,B,C$$ and their respective probability of solving the problem is $${1 \over 2},{1 \over 3}$$ a...