Parthasarathi Mukhopadhyay and Manabendra Nath Mukherjee Solutions for Exercise 1: EXERCISE

In an experiment of throwing a die twice, find the probability of getting a sum $5$ when it is given that the number $3$ has appeared at least once.

Muztaba and Sabnam appear in an interview for two vacancies in the same post. The probability of Muztaba's selection is $\frac{1}{4}$ and that of Sabnam's selection is $\frac{1}{3}$. What is the probability that both of them will be selected. (Write the answer in fraction.)

Find the probability that each of the following circuit will work. It is given that the switches $S_1$ and $S_2$ have respectively $85\%$ and $95\%$ chances of working.

What is the probability that the series circuit in the adjoining figure will work, when it is given that the switches $S_1, S_2, S_3$ work are $\frac{1}{2}, \frac{1}{4}, \frac{5}{6}$ respectively.

There are three switches $S_1,S_2,S_3$ in the switches circuit shown below. The probabilities that the switches work are $0.75,0.85 \mathrm{and} 0.95$ respectively. Determine the probability that the current can flow through the circuit

The probabilities that the three switches $S_1, S_2$ and $S_3$ in the switches circuit shown below work are respectively $\frac{1}{3}, \frac{2}{3}$ and $\frac{3}{4}$ respectively. Find the probability that the current can flow through the circuit.

A box contains $4$ red, $4$ black and $2$ white balls. Three balls are drawn from the box, one by one, without replacement. Find the probability that the third ball is white.

Arka, Ajad and Adam throw alternately a pair of coins in succession till one gets two heads and wins the game. Find their respective probabilities of winning the game, if Arka begins.