If the chance that any of the five telephone lines is busy at an instant is $0.01$, then what is the probability that all lines are busy? What is the probability that more than $3$ lines are busy?

The probability of a man hitting a target is $0.25$. He shoots $7$ times. What is the probability of his hitting at least twice?

During a war,$1$ in $10$ ships was sunk in the average in making a certain voyage. What is the probability that at least $3$ out of a convoy of $6$ ships would arrive safely?

A student answers $20$ true-false types of questions by tossing a fair coin. If the coin fall heads, he answers 'true' and if it falls tails he answers 'false'. Find the probability that he answers at least $12$ questions correctly.

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 $B\left(8, \frac{1}{4}\right)$.