JEE MAIN Probability Previous Year Questions (PYQs) – Page 7 of 8

The probability that a randomly chosen 5-digit number is made from exactly two digits is :

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 from the bag at random. The probability that all the balls drawn are white is:

Let \( S=\{w_1,w_2,\ldots\} \) be the sample space of a random experiment. Let the probabilities satisfy \[ P(w_n)=\frac{P(w_{n-1})}{2},\qquad n\ge 2. \] Let \[ A=\{\,2k+3\ell : k,\ell\in\mathbb{N}\,\},\qquad B=\{\,w_n : n\in A\,\}. \] Then \(P(B)\) is equal to:

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is:

The probability of selecting integers a$\in$[$-$ 5, 30] such that x² + 2(a + 4)x $-$ 5a + 64 > 0, for all x$\in$R, is :

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 outcomes is positive is:

In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he throws total a of 6 before B throws a total of 7 and B wins the game if he throws a total of 7 before A throws a total of six. The game stops as soon as either of the players wins. The probability of A winning the game is :

Let Ajay will not appear in JEE exam with probability $p=\dfrac{2}{7}$, while both Ajay and Vijay will appear in the exam with probability $q=\dfrac{1}{5}$. Then the probability that Ajay will appear in the exam and Vijay will not appear is:

An urn contains $5$ red and $2$ green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red is: