R D Sharma Solutions for Chapter: Probability, Exercise 7: EXERCISE

A manufacturer has three machine operators $A, B$ and $C$. The first operator $A$ produces $1\%$ defective items, whereas the other two operators $B$ and $C$ produce $5\%$ and $7\%$ defective items respectively. $A$ is on the job for $50\%$ of the time, $B$ on the job for $30\%$ of the time and $C$ on the job for $20\%$ of the time. A defective item is produced. What is the probability that it was produced by$A?$

An item is manufactured by three machines $A, B$ and $C$. Out of the total number of items manufactured during a specified period, $50\%$ are manufactured on machine $A$, $30\%$ on $B$ and $20\%$ on $C$. $2\%$ of the items produced on $A$ and $2\%$ of items produced on $B$ are defective and $3\%$ of these produced on $C$are defective. All the items stored at one godown. One item is drawn at random and is found to be defective. What is the probability that it was manufactured on machine $A?$

There are three coins. One is two-headed coin (having head on both faces), another is biased coin that comes up heads $75\%$ of the times and third is also a biased coin that comes up tail $40\%$ of the times. One of the three coins is chosen at random and tossed, and it shows heads. What is the probability that it was the two-headed coin?

In a factory, machine $A$ produces $30\%$ of the total output, machine $B$ produces $25\%$ and the machine $C$ produces the remaining output. If defective items produced by machines $A, B$ and $C$ are $1\%, 1.2\%, 2\%$ respectively. Three machines working together produce $10000$ items in a day. An item is drawn at random from a day's output and found to be defective. Find the probability that it was produced by machine $B?$

A company has two plants to manufacture bicycles. The first plant manufactures $60\%$ of the bicycles and the second plant $40\%$. Out of the $80\%$ of the bicycles are rated of standard quality at the first plant and $90\%$ of standard quality at the second plant. A bicycle is picked up at random and found to be standard quality. Find the probability that it comes from the second plant.

Three urns $A, B$ and $C$ contain $6$ 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 ball was drawn from urn $A$.

For $A, B$ and $C$ the chances of being selected as the manager of a firm are in the ratio $4:1:2$ respectively. The respective probabilities for them to introduce a radical change in marketing strategy are $0.3, 0.8$ and $0.5$. If the change does take place, find the probability that it is due to the appointment of $B$ or $C$.

By examining the chest x-ray , probability that T.B is detected when a person is actually suffering is $0.99$. The probability that the doctor diagnoses incorrectly that a person has T.B. on the basis of x-ray is $0.001$. In a certain city $1$ in $1000$ persons suffers from T.B. A person is selected at random is diagnosed to have T.B. What is the chance that he actually has T.B.?