JEE Main 2002 — Probability & Statistics

$A$ and $B$ are events such that $P(A \cup B)=3 / 4, P(A \cap B)=1 / 4, P(\bar{A})=2 / 3$ then $P(\bar{A} \cap B)$ is

A problem in mathematics is given to three students $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and their respective probability of solving the problem is $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$. Probability that the problem is solved is

In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls?

A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is