R S Aggarwal Solutions for Exercise 1: EXERCISE

A man can hit a bird, once in $3$ shots. On this assumption he fires $3$ shots. What is the value of $k$, if the chance of hitting at least one bird is $\frac{k}{27}$.

If the probability that a man aged $60$ will live to be $70$ is $0.65$, what is the probability that out of $10$ men, now $60$, at least $8$ will live to be $70$?

A bag contains $5$ white, $7$ red $8$ black balls. If four balls are drawn one by one with replacement, what is the probability that none is white

A bag contains $5$ white, $7$ red $8$ black balls. If four balls are drawn one by one with replacement, what is the probability that all are white

A bag contains $5$ white, $7$ red $8$ black balls. If four balls are drawn one by one with replacement, the probability that at least one is white is $\frac{k}{256}$. Find the value of $k$.

A policeman fires $6$ bullets at a burglar. The probability that the burglar will be hit by a bullet is $0.6$. What is the probability that burglar is still unhurt?

The mean and variance of a binomial distribution are $4$ and $\left(\frac{4}{3}\right)$ respectively. Find $\mathrm{P}(\mathrm{X}\ge 1)$.

For a binomial distribution, the mean is $6$ and the standard deviation is $\sqrt{2}$. If the probability of getting $5$ successes is ${}^{9}C_5\frac{k}{3^9}$, then find the value of $k$.