JEE Main · 2026 · 06 Apr 2026 · Shift 1 · Probability

A random variable $X$ takes values $0,1,2,3$ with probabilities $\frac{2a+1}{30}$, $\frac{8a-1}{30}$, $\frac{4a+1}{30}$, b respectively, where $a,b\in \mathbf{R}$. Let $\mu$ and $\sigma$ respectively be the mean and standard deviation of X such that ${\sigma }^2+{\mu }^2=2$.
Then …

Two distinct numbers a and b are selected at random from $1,2,3,\dots ,50$. The probability, that their product ab is divisible by 3, is

If a random variable $x$ has the probability distribution

then …

From the first 100 natural numbers, two numbers first a and then b are selected randomly without replacement. If the probability that $a-b\ge 10$ is $\frac{m}{n},\gcd (m,n)=1$, then $m+n$ is equal to ______.

Bag A contains 9 white and 8 black balls, while bag B contains 6 white and 4 black balls. One ball is randomly picked up from the bag B and mixed up with the balls in the bag A. Then a ball is randomly drawn from the bag A. If the probability, that the ball drawn is white, is …

From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is :-