Embibe Experts Solutions for Chapter: Probability, Exercise 3: EXERCISE-3

A room has three electric lamps. From a collection of $10$ electric bulbs of which $6$ are good $3$ are selected at random & put in the lamps. Find the probability that the room is lighted is $\frac{a}{b}$, then $\left(a+b\right)$ is

A bomber wants to destroy a bridge. Two bombs are sufficient to destroy it. If four bombs are dropped, what is the probability that it is destroyed, if the chance of a bomb hitting the target is $0.4$ is $\frac{a}{5^4}$, then $a$ is

The chance of one event happening is the square of the chance a $2^{\mathrm{nd}}$ event, but odds against the first are the cubes of the odds against the $2^{\mathrm{nd}}$. Chances of each (Assume that both events are neither sure nor impossible) are $\frac{1}{x}$ and $\frac{1}{y}$, then $\left(x+y\right)$ is

A box contains $5$ radio tubes of which $2$ are defective. The tubes are tested one after the other until the $2$ defective tubes are discovered. The probability that the process stopped on the

(a) second test is $\frac{1}{a},$ then $a$ is

(b) third test is $\frac{115}{b},$ then $b$ is

(c) If the process stopped on the third test, find the probability that the first tube is non-defective is $\frac{x}{y}$, then $\left(x+y\right)$ is

Anand plays with Karpov $3$ games of chess. The probability that he wins a game is $0.5$, looses with probability $0.3$ and ties with probability $0.2$. If he plays $3$ games then the probability that he wins atleast two games is

An aircraft gun can take a maximum of four shots at an enemy's plane moving away from it. The probability of hitting the plane at first, second, third & fourth shots are $0.4, 0.3, 0.2 \& 0.1$ respectively. What is the probability that the gun hits the plane is $\frac{x}{100}$, then integral part of $x$ is

One hundred management students who read at least one of the three business magazines are surveyed to study the readership pattern. It is found that $80$ read Business India, $50$ read Business World and $30$ read Business Today. Five students read all the three magazines. A students was selected randomly. Find the probability that he reads exactly two magazines is $\frac{1}{a}$, then $a$ is

An author writes a good book with a probability of $\frac{1}{2}$. If it is good it is published with a probability of $\frac{2}{3}$. If it is not, it is published with a probability of $\frac{1}{4}$. Find te probability that he will get atleast one book published if he writes two is $\frac{a}{576}$, then $a$ is