$A$ coin is tossed $n$ times. The probability of getting a head at least once is greater than $0.8$. Then, the least value of such $n$ is:

When two dice are rolled, let $x$ be the probability that the sum of the numbers appearing on the dice is at most $7$. Let $y$ be the probability of getting a sum of $7$ at least once when a pair of dice are rolled $n$ times. In order to have $y > x$, the minimum value of $n$ is

If the probability that a student is not a swimmer is $\frac{1}{5}$,then the probability that out of $5$ students one is a swimmer is

$A$ random experiment is conducted five times. If the number of successes of the experiment follows a binomial distribution such that the difference between the mean and variance of the successes is $\frac{5}{9}$, then the probability of getting at most two successes is

In order to get a head at least once with probability $\geq 0.9$, the minimum number of times an unbiased coin needs to be tossed is

If $20 \%$ of the bolts produced by a machine are defective, then the probability that out of $4$ bolts chosen at random, less than $2$ bolts will be defective, is