Probability

13 solved problems from JEE previous year papers.

Probability

Aman and Bhuvan Throw a Pair of Dice Alternately. In Order to Win They Have to Get a Sum of 8. Find Their Respective Probabilities of Winning if Aman Starts the Game

Aman and Bhuvan throw a pair of dice alternately, and whoever first gets a sum of 8 wins. Find each player’s probability of…
Probability

In a Class of 60 Students, 30 Opted for NCC, 32 Opted for NSS and 24 Opted for Both. If One Student Is Selected at Random, Find the Probability That the Student Opted for NCC or NSS, for Neither, and for NSS but Not NCC

NCERT Class 11 Probability Ex 11.2 Q21: 60 students, 30 in NCC, 32 in NSS, 24 in both — find P(NCC or NSS), P(neither) and P(NSS…
Probability

Suppose a Girl Throws a Die. If She Gets 5 or 6 She Tosses a Coin Three Times and Notes the Number of Heads; if She Gets 1, 2, 3 or 4 She Tosses a Coin Once. If She Obtained Exactly One Head, What Is the Probability That She Threw 1, 2, 3 or 4 With the Die

A girl throws a die: on 5 or 6 she tosses a coin 3 times, otherwise once. Given she got exactly one head, find the probability…
ISC 2011

A Box Contains 4 Red and 5 Black Marbles. Find the Probability Distribution of the Red Marbles in a Random Draw of Three Marbles. Also Find the Mean, Variance and Standard Deviation

A box has 4 red and 5 black marbles. Find the probability distribution of the number of red marbles in a random draw of 3, then…
ISC 2010

There Are Two Bags. One Bag Contains Six Green and Three Red Balls, the Second Bag Contains Five Green and Four Red Balls. One Ball Is Transferred From the First Bag to the Second, Then One Ball Is Drawn From the Second Bag. Find the Probability That It Is a Red Ball

Bag 1 has 6 green, 3 red balls; Bag 2 has 5 green, 4 red. One ball moves from Bag 1 to Bag 2, then one is drawn from Bag 2. Find…
Probability

A Person Has Undertaken a Construction Job. The Probabilities Are 0.65 That There Will Be a Strike, 0.80 That the Job Will Be Completed on Time if There Is No Strike, and 0.32 if There Is a Strike. Find the Probability the Job Will Be Completed on Time

A construction job has 0.65 probability of a strike, with different completion probabilities depending on whether there’s a…
Probability

A Committee of 4 Persons Has to Be Chosen From 8 Boys and 6 Girls, Consisting of at Least One Girl. Find the Probability That the Committee Consists of More Girls Than Boys

A committee of 4 is chosen from 8 boys and 6 girls, with at least one girl. Find the probability the committee has more girls…
Probability

Two Dice Rolled — P(Even on First Die or Total of 8)

Two dice are rolled once. Find the probability of getting an even number on the first die or a total of 8, using the addition…
Probability

Proof: P(A∪B) = 1 − P(A′)·P(B′) for Independent Events

A derivation of P(A∪B)=1−P(A’)P(B’) for independent events A and B, from NCERT Example 14, using the standard union…
Probability

2×2 Matrix With Entries 0 or 1 — Variance of the Determinant

A 2×2 matrix has entries from {0,1}. Let X be its determinant. Find the variance of X by listing all 16 matrices and their…
Probability

Out of 16 Squares on a Board, Two Squares Are Chosen at Random. The Probability That They Have No Side in Common Is

A 4×4 board has 16 squares. Two are chosen at random. Find the probability they share no side, by counting adjacent pairs…
Probability

Two Persons A and B Throw a Pair of Dice Alternately. A Wins if He Throws a Sum of 5 Before B Throws a Sum of 8. If A Throws First, the Probability That A Wins Is

A and B alternately throw a pair of dice; A wins by throwing sum 5 before B throws sum 8. Full solution using independent events…
Probability

A Committee of 4 Students Is Selected at Random From a Group Consisting of 8 Boys and 4 Girls. Given That There Is at Least One Girl in the Committee, Find the Probability That There Are Exactly 2 Girls

A committee of 4 is chosen from 8 boys and 4 girls. Given at least one girl is selected, find the probability of exactly 2 girls,…