If the mean and variance of a binomial variate $X$ are $8$ and $4$ respectively,then $P(X < 3)$ equals to

$A$ 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:

An unbiased coin is tossed $8$ times. The probability that head appears consecutively at least $5$ times is

Suppose $X$ has a binomial distribution $B(6, 1/2)$. Show that $X=3$ is the most likely outcome.
(Hint: $P(X=3)$ is the maximum among all $P(x_i)$,where $x_i = 0, 1, 2, 3, 4, 5, 6$)

$A$ fair coin is tossed $n$ times. Let $X$ be the number of times head is observed. If $P(X = 4), P(X = 5)$ and $P(X = 6)$ are in $H.P.$,then $n$ is equal to

If the mean and variance of a binomial variate $X$ are $2$ and $1$ respectively,then the probability that $X$ takes a value greater than $1$ is