Probability – JEE Advanced Previous Year Questions with Solutions

JEE Advanced Previous Year Questions of Math with Solutions are available at eSaral. Practicing JEE Advanced Previous Year Papers Questions of mathematics will help the JEE aspirants in realizing the question pattern as well as help in analyzing weak & strong areas.

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Let $\mathrm{U}_{1}$ and $\mathrm{U}_{2}$ be two urns such that $\mathrm{U}_{1}$ contains 3 white and 2 red balls, and $\mathrm{U}_{2}$ contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from $\mathrm{U}_{1}$ and put into $\mathrm{U}_{2} .$ However, if tail appears then 2 balls are drawn at random from $\mathrm{U}_{1}$ and put into $\mathrm{U}_{2} .$ Now 1 ball is drawn at random from $\mathrm{U}_{2} .$

A box $\mathrm{B}_{1}$ contains 1 white ball, 3 red balls and 2 black balls. Another box $\mathrm{B}_{2}$ contains white balls, 3 red balls and 4 black balls. A third box $B_{3}$ contains 3 white balls, 4 red balls and 5 black balls.

Box 1 contains three cards bearing numbers, 1,2,3 ; box 2 contains five cards

bearing numbers 1,2,3,4,5; and box 3 contains seven cards bearing numbers 1,2,3,4,5,6,7. A card is drawn from each of the boxes. Let xi be the number on the card drawn from the ith box, i = 1,2,3.

Let $n_{1}$ and $n_{2}$ be the number of red and black balls respectively, in box I. Let $n_{3}$ and $n_{4}$ be the number of red and black balls, respectively, in box II.


Football teams $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $\mathrm{T}_{1}$ winning, drawing and losing a game against $\mathrm{T}_{2}$ are $\frac{1}{2}, \frac{1}{6}$ and $\frac{1}{3},$ respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let $X$ and $Y$ denote the total points scored by teams $\mathrm{T}_{1}$ and $\mathrm{T}_{2},$ respectively, after two games

There are five students $S_{1}, S_{2}, S_{4}$ and $S_{5}$ in a music class and for them there are five sets $\mathrm{R}_{1}, \mathrm{R}_{2}, \mathrm{R}_{3}, \mathrm{R}_{4}$ and $\mathrm{R}_{5}$ arranged in a row, where initially the seat $\mathrm{R}_{\mathrm{i}}$ is allotted to the student $S_{i}, i=1,2,3,4,5 .$ But, on the examination day, the five students are randomly allotted the five seats.

(There are two questions based on Paragraph “A”. the question given below is one of them)

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