R D Sharma Solutions for Chapter: Probability, Exercise 5: EXERCISE

Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that first ball is black and second is red.

Kamal and Monika appeared for an interview for two vacancies. The probability of Kamal's selection is $\frac{1}{3}$ and that of Monika's selection is $\frac{1}{5}$. Find the probability that both of them will be selected.

Kamal and Monika appeared for an interview for two vacancies. The probability of Kamal's selection is $\frac{1}{3}$ and that of Monika's selection is $\frac{1}{5}$. Find the probability that only one of them will be selected.

A husband and wife appear in an interview for two vacancies for the same post. The probability of husband's selection is $\frac{1}{7}$ and that of wife's selection is $\frac{1}{5}$. What is the probability that both of them will be selected ?

A bag contains $4$ white, $7$ black and $5$ red balls. $4$ balls are drawn with replacement. What is the probability that at least two are white?

A bag contains $4$ red and $5$ black balls, a second bag contains $3$ red and $7$ black balls. One ball is drawn at random from each bag, find the probability that the balls are of the same colour.

Fatima and John appear in an interview for two vacancies for the same post. The probability of Fatima's selection is $\frac{1}{7}$ and that of John's selection is $\frac{1}{5}$ What is the probability that both of them will be selected?

$A$ and $B$ throw a pair of dice alternately. $A$ wins the game if he gets a total of $7$ and $B$ wins the game if he gets a total of $10$. If $A$ starts the game, then find the probability that $B$ wins.