If $A, B, C$ are three mutually exclusive and exhaustive events of an experiment such that $P(A)=2 P(B)=3 P(C)$,then $P(B)$ is equal to

There are two children in a family. The probability that both of them are boys is

The probability of drawing a white ball from a bag containing $3$ black balls and $4$ white balls is:

Six faces of an unbiased die are numbered with $2, 3, 5, 7, 11$ and $13$. If two such dice are thrown, then the probability that the sum on the uppermost faces of the dice is an odd number 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

The probability of hitting a target by three marksmen are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. The probability that one and only one of them will hit the target when they fire simultaneously,is