A die is thrown thrice. If getting 1 or 6 in a single throw is considered as success, then the variance of the number of successes is

In a hospital, on an average if there are 35 births in a weak, then the probability that there will be less than 3 births in a day, is

If $A$ and $B$ are events of a sample space such that $P(A \cup B)=\frac{3}{4}, P(A \cap B)=\frac{1}{4}$ and $P(\bar{A})=\frac{2}{3}$, then $P(\bar{A} \cap B)$ is

Let $X$ and $Y$ be two events of a sample space such that $P(X)=\frac{1}{3}, P(X / Y)=\frac{1}{2}$ and $P(Y / X)=\frac{2}{5}$ then