JEE MAIN Probability Previous Year Questions (PYQs) – Page 1 of 9

Let $E_1, E_2, E_3$ be three mutually exclusive events such that $P(E_1)=\dfrac{2+3p}{6}$, $P(E_2)=\dfrac{2-p}{8}$ and $P(E_3)=\dfrac{1-p}{2}$. If the maximum and minimum values of $p$ are $p_1$ and $p_2$, then $(p_1+p_2)$ is equal to:

Let $A$ and $B$ be two events such that $P(\overline{A\cup B})=\dfrac{1}{6}$, $P(A\cap B)=\dfrac{1}{4}$ and $P(\overline{A})=\dfrac{1}{4}$, where $\overline{A}$ stands for the complement of the event $A$. Then the events $A$ and $B$ are :

Two dice are thrown independently. Let \(A\) be the event that the number on the \(1^{\text{st}}\) die is less than the number on the \(2^{\text{nd}}\) die; \(B\) be the event that the number on the \(1^{\text{st}}\) die is even and that on the \(2^{\text{nd}}\) die is odd; and \(C\) be the event that the number on the \(1^{\text{st}}\) die is odd and that on the \(2^{\text{nd}}\) die is even. Then:

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:

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 $7$ but not divisible by $5$, then $9p$ is equal to :

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 are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box $B$ is :

The coefficients $a,b,c$ in the quadratic $ax^{2}+bx+c=0$ are chosen from the set ${1,2,3,4,5,6,7,8}$. The probability that the equation has repeated roots is:

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

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

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 from it at random, are found to be 1 red and 1 black. If the probability that both balls come from Bag A is ${6 \over {11}}$, then n is equal to __________.