R S Aggarwal Solutions for Exercise 1: EXERCISE

In a certain college, $4\%$ of boys and $1\%$ of girls are taller than $1.75 \mathrm{meters}$. Furthermore, $60\%$ of the students are girls. If a student is selected at random and is taller than $1.75 \mathrm{meters}$, what is the probability that the selected student is a girl?

In a class, $5\%$ of the boys and $10\%$ of the girls have an$IQ$ of more than $150$. In this class, $60\%$ of the students are boys. If a student is selected at random and found to have $IQ$ of more than $150$, find the probability that the student is a boy.

Suppose $5\%$ of men and $0.25\%$ of women have grey hair. A grey-haired person is selected at random. What is the probability of this person being male? Assume that there is an equal number of males and females.

Two groups are competing for the positions on the board of directors of a corporation. The probabilities that the first and the second groups will win are $0.6$ and $0.4$, respectively. Further, if the first group wins, the probability of introducing a new product is $0.7$, and when the second groups win, the corresponding probability is $0.3$. Find the probability that the new product introduced was by the second group.

A bag $A$ contains $1$ white and $6$ red balls. Another bag contains $4$ white and $3$ red balls. One of the bags is selected at random, and a ball is drawn from it, which is found to be white. Find the probability that the ball is drawn is from bag $A$.

Three urns $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ contains $6$ red and $4$ white; $2$ red and $6$ white; and $1$ red and $5$ white balls respectively. An urn is chosen at random, and a ball is drawn. If the ball drawn is found to be red, find the probability that the balls was drawn from the first urn $\mathrm{A}$.

An insurance company insured $2000$ scooters and $3000$ motorcycles. The probability of an accident involving a scooter is $0.01$, and that of motorcycles is $0.02$. An insured vehicle met with an accident. Find the probability that the accident vehicle was a motorcycle.

In a bulb factory, machines $\mathrm{A}, \mathrm{B}$ and $C$ manufactures $60\%, 30\%$ and $10\%$ bulbs respectively. Out of these bulbs $1\%, 2\%$ and $3\%$ of the bulbs produced respectively by $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are found to be defective. A bulb is picked up at random from the total production and found to be defective. Find the probability that this bulb was produced by machine $\mathrm{A}$.