Probability Basics: JEE Questions & Solutions

Let the mean and variance of 7 observations 2, 4, 10, x, 12, 14, y, where x y, be 8 and 16 respectively. Two numbers are chosen from 1, 2,…

Two distinct numbers a and b are selected at random from 1, 2, 3,, 50. The probability that their product ab is divisible by 3 is

From the first 100 natural numbers, two numbers first a and then b are selected randomly without replacement. If the probability that a - b…

Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is picked from B and put in A. Then a…

Let S be a set of 5 elements and P(S) denote the power set of S. Let E be the event of choosing an ordered pair (A,B) from P(S) P(S) such…

One die has two faces marked 1, two faces marked 2, one face marked 3, and one face marked 4. Another die has one face marked 1, two faces…

A board has 16 squares as shown in the figure. Out of these 16 squares, two squares are chosen at random. The probability that they have no…

A and B alternately throw a pair of dice. A wins if he throws a sum of 5 before B throws a sum of 8, and B wins if he throws a sum of 8…

Let A = [aij] be a square matrix of order 2 with entries either 0 or 1. Let E be the event that A is an invertible matrix. Then the…

Two numbers k1 and k2 are randomly chosen from the set of natural numbers. Then, the probability that the value of i^k1 + i^k2 (where i =…

Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, one word is selected…

Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1…

Three distinct numbers are selected randomly from the set 1, 2, 3,, 40. If the probability that the selected numbers are in an increasing…

The probability of forming a 12 persons committee from 4 engineers, 2 doctors, and 10 professors containing at least 3 engineers and at…

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 3), and…

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

A fair die is thrown until the number 2 appears. What is the probability that 2 appears in an even number of throws?

An integer is chosen at random from the integers 1, 2, 3,, 50. The probability that the chosen integer is a multiple of at least one of 4,…

Two integers x and y are chosen with replacement from the set 0,1,2,,10. Then the probability that |x - y| 5 is:

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

Two integers x and y are chosen with replacement from the set 0,1,2,,10. Then the probability that |x-y|5 is:

An integer is chosen at random from the integers 1, 2, 3,..., 50. The probability that the chosen integer is a multiple of at least one of…

The coefficients a, b, and c in the quadratic equation ax^2 + bx + c = 0 are chosen from the set 1, 2, 3, 4, 5, 6, 7, 8. The probability of…

If an unbiased dice is rolled thrice, then the probability of getting a greater number in the i-th roll than the number obtained in the…

If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly…

Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that N-2, 3N, N+2 are in geometric…

Fifteen football players of a club are given 15 T-shirts with their names written on the back. If the players pick up the T-shirts…

Let S = W1, W2, be the sample space associated with a random experiment. Let P(Wn) = P(Wn-1)2, n 2. Let A = 2k + 3l; k, l N and B = Wn; n…

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…

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

Let A be the event that the absolute difference between two randomly chosen real numbers in the sample space [0, 60] is less than or equal…

Two dice are thrown independently. Let A be the event that the number appeared on the 1^ st die is less than the number appeared on the 2^…

Three dice are rolled. If the probability of getting different numbers on the three dice is pq, where p and q are co-prime, then q - p is…

Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that 2N < N! is m/n, where m and n are coprime,…

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…