The probability that a person who undergoes a bypass surgery will recover is $0.6$. The probability that of the $6$ patients who undergo similar operations,half of them will recover is:

$A$ fair die is thrown $4$ times. If getting a prime number on the die is considered as a success, then the probability of getting no success at all is ...

In an examination,$20$ questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads,he answers 'true'; if it falls tails,he answers 'false'. Find the probability that he answers at least $12$ questions correctly.

Let $X$ be a random variable having binomial distribution $B(7, p)$. If $P(X=3) = 5P(X=4)$,then the sum of the mean and the variance of $X$ is

Consider $5$ independent Bernoulli trials,each with a probability of success $p$. If the probability of at least one failure is greater than or equal to $31/32$,then in which interval does $p$ lie?

$A$ rifleman is firing at a distant target and has only $10 \%$ chance of hitting it. The least number of rounds he must fire to have more than $50 \%$ chance of hitting it at least once, is