The probability that a bulb produced by a factory will fuse after $150$ days of use is $0.05$. Find the probability that out of $5$ such bulbs,at least one will fuse after $150$ days.

The random variable $X$ follows a binomial distribution $B(n, p)$ for which the difference between the mean and the variance is $1$. If $2 P(X=2) = 3 P(X=1)$,then $n^2 P(X > 1)$ is equal to $......$.

The probability that a person is not a sportsperson is $\frac{1}{6}$. Then the probability that out of the $6$ members of the family,$5$ are sportspersons is

$A$ coin is tossed $n$ times. If the probability of getting $6$ heads is equal to the probability of getting $8$ heads,then find the value of $n$.

$A$ fair coin is tossed $100$ times. The probability of getting tails an odd number of times 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