The probability of an event $A$ happening in one trial is $0.4$. The probability that the event $A$ happens at least once in three independent trials is

The probability of success $p$ for the Binomial distribution satisfying the relation $4 P(X=4) = P(X=2)$ with parameter $n=6$ is

Consider $5$ independent Bernoulli trials each with probability of success $p$. If the probability of at least one failure is greater than or equal to $\frac{31}{32}$,then $p$ lies in the interval:

If $15$ coins are tossed,then the probability of getting $10$ heads is:

The mean and variance of a binomial distribution are $4$ and $3$ respectively. Then,the probability of getting exactly six successes in this distribution is:

Given $X \sim B(n, p)$,if $E(X) = 4$ and $\operatorname{Var}(X) = 2.4$,then $n = $