The probability of getting $4$ heads in $8$ throws of a coin 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:

$A$ box contains $30$ toys of the same size,in which $10$ toys are white and the remaining toys are blue. $A$ toy is drawn at random from the box and it is replaced in the box after noting down its colour. If $5$ toys are drawn in this way,then the probability of getting at most $2$ white toys is

Tom and Jerry play a game of alternately throwing an unfair coin. The first one to get a head wins. If Tom starts the game,he has a $62.5 \%$ chance of winning. Suppose this coin is tossed $5$ times,then the probability of getting exactly $3$ heads is

The probability that a student is not a swimmer is $\frac{1}{5}$. The probability that out of $5$ students selected at random,$4$ are swimmers is:

Consider the following events:
$E_1$: Six fair dice are rolled and at least one die shows six.
$E_2$: Twelve fair dice are rolled and at least two dice show six.
Let $p_1$ be the probability of $E_1$ and $p_2$ be the probability of $E_2$. Which of the following is true?