Skip to main content
Yukti Vault

Statistics & Probability

Probability: JEE Main & Advanced PYQs

372 previous year questions on Probability from JEE Main and JEE Advanced papers, each with its exam and year, an answer and a solution.

Practice this chapter

Questions 351-372 of 372

  1. In a tournament, a team plays $10$ matches with probabilities of winning and losing each match as $\dfrac{1}{3}$ and $\dfrac{2}{3}$ respectively. Let $x$ be the number …
  2. If the mean of the following probability distribution of a random variable $X$ …
  3. From a lot of $10$ items, which include $3$ defective items, a sample of $5$ items is drawn at random. Let the random variable $X$ denote the number of defective items …
  4. The coefficients $a,b,c$ 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 this equation having repeated roots …
  5. The coefficients $a,b,c$ in the quadratic equation $ax^{2}+bx+c=0$ are from the set $\{1,2,3,4,5,6\}$. If the probability of this equation having one real root bigger …
  6. In a bombing attack, there is $50\%$ chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the …
  7. 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 positive common …
  8. A coin is tossed three times. Let $X$ denote the number of times a tail follows a head. If $\mu$ and $\sigma^{2}$ denote the mean and variance of $X$, then the value of …
  9. Two balls are selected at random one by one without replacement from a bag containing $4$ white and $6$ black balls. If the probability that the first selected ball is …
  10. If $A$ and $B$ are two events such that $P(A\cap B)=0.1$, and $P(A\mid B)$ and $P(B\mid A)$ are the roots of the equation $12x^{2}-7x+1=0$, then the value of …
  11. 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 marked $2$, two faces …
  12. Let $A=[a_{ij}]$ 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 probability $P(E)$ is :
  13. 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 at random. The probability …
  14. Bag $B_1$ contains $6$ white and $4$ blue balls, Bag $B_2$ contains $4$ white and $6$ blue balls, and Bag $B_3$ contains $5$ white and $5$ blue balls. One of the bags is …
  15. A dice is tossed $5$ times. Getting an odd number is considered a success. Then the variance of the distribution of success is :
  16. The mean and variance of a random variable $X$ having binomial distribution are $4$ and $2$ respectively, then $P(X=1)$ is :
  17. The mean and the variance of a binomial distribution are $4$ and $2$ respectively. Then the probability of $2$ successes is :
  18. A pair of fair dice is thrown independently three times. The probability of getting a score of exactly $9$ twice is :
  19. In a binomial distribution $B\left(n,p=\frac14\right)$, if the probability of at least one success is greater than or equal to $\frac{9}{10}$, then $n$ is greater than :
  20. Consider $5$ independent Bernoulli's trials each with probability of success $p$. If the probability of at least one failure is greater than or equal to $\frac{31}{32}$ …
  21. A multiple choice examination has $5$ questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get $4$ …
  22. 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 $C$ occurs …

Other chapters