JEE Main 2017 — Probability & Statistics

If two different numbers are taken from the set ${0,1,2,3,.....,10}$; then the probability that their sum as well as absolute difference are both multiple of $4$, is:

Let $E&F$ be two independent events. The probability that $E&F$ happen is $\frac{1}{12}$ and the probability that neither $E$ nor $F$ happens is $\frac{1}{2}$ , then a value of $\frac{P(E)}{P(F)}$ is:

The mean age of $25$ teachers in a school is $40$ years. A teacher retires at the age of $60$ years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is $39$ years, then the age (in years) of the newly appointed teacher is

The sum of $100$ observations and the sum of their squares are $400&2475$, respectively. Later on, three observations $3,4&5$ were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is

Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target are $\frac{3}{4},\frac{1}{2}$ and $\frac{5}{8}$ respectively, then the probability that the target is hit by P or Q but not by R is: