The probability of a man hitting a target is $0.25$. How many times must he fire so that the probability of his hitting the target at least once is greater than $\frac{2}{3}$ ?

The probability of India winning a test match against West-Indies is $\frac{1}{2}$. Find the probability that in a test match series India's second win occurs at the third test.

A fair die is tossed eight times. The probability that a third six is observed on the eighth throw is $\frac{7}{72}{\left(\frac{5}{6}\right)}^k$, then find the value of $k$ .

Is it possible that the mean of a binomial distribution is $15$ and its standard deviation is $5$ ?

Find the mean of the Binomial distribution $B\left(8, \frac{1}{4}\right)$.

If the probability of a defective bolt is $0.1$, then find the mean and the standard deviation for the number of defective bolts in a total of $400$ bolts.

Find the expectation of number of heads in 20 tosses of a fair coin.

A die is tossed twice. A success is defined as getting an odd number on a random toss. Find the mean and variance of the number of successes.