Let $X$ be the random variable taking values $1,2, \ldots n$ for a fixed positive integer $n$. If $P(X=k)=\frac{1}{n}$ for $1 \leq k \leq n$, then the variance of $X$ is

A radar system can detect an enemy plane in one out of ten consecutive scans.

The probability that it can detect an enemy plane atleast twice in four consecutive scans is

A company representative is distributing 5 identical samples of a product among 12 houses in a row such that each house gets at most one sample. The probability that no two consecutive house get one sample is

38. $A$ and $B$ are two independent events of a random experiment and $P(A)>P(B)$.

If the probability that both $A$ and $B$ occurs is $\frac{1}{6}$ and neither of them occurs is $\frac{1}{3}$, then the probability of the occurance of $B$ is