From a lot containing $10$ defective and $90$ non-defective bulbs, $8$ bulbs are selected one by one with replacement. Then the probability of getting at least $7$ defective bulbs is:

Let in a Binomial distribution,consisting of $5$ independent trials,probabilities of exactly $1$ and $2$ successes be $0.4096$ and $0.2048$ respectively. Then the probability of getting exactly $3$ successes is equal to

Two cards are drawn successively with replacement from a fair deck of $52$ cards. Let $X$ denote the number of kings obtained when two cards are drawn. Then $E(X^2) = $

$A$ manufacturer of locks knows that $2 \%$ of his product is defective. If he sells the locks in boxes each with $100$ locks and guarantees that not more than $2$ locks will be defective in a box,then the probability that a box will fail to meet the guaranteed quality is

$A$ random variable $X$ follows a binomial distribution in which the difference between its mean and variance is $1$. If $2 P(X=2)=3 P(X=1)$,then $n^2 P(X>1)=$

An objective type test paper has $5$ questions. Out of these $5$ questions, $3$ questions have four options each $(a, b, c, d)$ with one option being the correct answer. The other $2$ questions have two options each, namely true and false. $A$ candidate randomly ticks the options. Then, the probability that he/she will tick the correct option in at least four questions, is