$A$ binary number is made up of $16$ bits. The probability of an incorrect bit appearing is $p$ and the errors in different bits are independent of one another. The probability of forming an incorrect number is

$A$ die is thrown twice. If getting a number greater than $4$ on the die is considered a success,then the variance of the probability distribution of the number of successes is

If $X \sim B(5, p)$ is a binomial variate such that $P(X=3)=P(X=4)$,then $P(|X-3| < 2)=$

Two cards are drawn successively with replacement from a well-shuffled pack of $52$ cards. The mean of the number of tens is:

Numbers are selected at random,one at a time from the two-digit numbers $00, 01, 02, \dots, 99$ with replacement. An event $E$ occurs only if the product of the two digits of a selected number is $24$. If four numbers are selected,then the probability that the event $E$ occurs at least $3$ times is:

$A$ student writes an examination which contains $8$ true or false questions. If he answers $6$ or more questions correctly,he passes the examination. If the student answers all the questions,then the probability that he fails in the examination is