$A$ bag contains books numbered $1$ to $20$. Three books are drawn from the bag with replacement. The probability that the largest number on the books is $7$ is:

If the mean and variance of a binomial variate $X$ are $\frac{4}{3}$ and $\frac{8}{9}$ respectively,then $P(X=2)=$

The probability that a student gets distinction in a Mathematics test is $\frac{2}{3}$. If five such tests are conducted over a certain period of time,then the probability that he gets distinction in at least $3$ tests is

$A$ target is to be destroyed in a bombing exercise and there is a $75 \%$ chance that a bomb will hit the target. Assuming that two direct hits are required to destroy the target completely, the minimum number of bombs to be dropped in order that the probability of destroying the target is not less than $99 \%$, is

$A$ lot of $100$ bulbs contains $10$ defective bulbs. Five bulbs are selected at random from the lot and sent to a retail store. The probability that the store will receive at most one defective bulb is:

The probability of getting a success in a trial is five times that of a failure. The probability of getting at most one success in $5$ trials is: