If $X$ has a binomial distribution with mean $np$ and variance $npq$,then $\frac{P(X = k)}{P(X = k - 1)}$ is

$A$ test consists of $6$ multiple choice questions,each having $4$ alternative answers of which only one is correct. The number of ways in which a candidate answers all $6$ questions such that exactly $4$ of the answers are correct is:

$A$ fair coin is tossed $100$ times. The chance of getting a head an even number of times is

The probability of a man hitting a target is $\frac{2}{3}$. What is the minimum number of times he must fire so that the probability of hitting the target at least once is more than $90 \%$?

Let a biased coin be tossed $5$ times. If the probability of getting $4$ heads is equal to the probability of getting $5$ heads,then the probability of getting at most two heads is

$A$ bag contains $4$ red and $3$ black balls. One ball is drawn and then replaced in the bag and the process is repeated. Let $X$ denote the number of times a black ball is drawn in $3$ draws. Assuming that at each draw each ball is equally likely to be selected,then the probability distribution of $X$ is given by: