Amit M Agarwal Solutions for Chapter: Advanced Probability, Exercise 2: Work Book Exercise 16.2

Probability that $A$ speaks truth is $\frac{4}{5}$. A coin is tossed, $A$ reports that a head appears. The probability that actually there was head, is

A company has two plants to manufacture televisions. Plant $\mathrm{I}$ manufactures $70\%$ of televisions and plant $\mathrm{II}$ manufactures $30\%$. At plant $\mathrm{I}$, $80\%$ of the televisions are rated as of standard quality and at plant $\mathrm{II}$, $90\%$ of the televisions are rated as of standard quality. A television is chosen at random and is found to be of standard quality. The probability that it has come from plant $\mathrm{II}$, is

Three machines $E_1$, $E_2$ and $E_3$ in a certain factory produce $50\%$, $25\%$ and $25\%$, respectively of the total daily output of electric tubes. It is known that $4\%$ of the tubes produced one each of machines $E_1$ and $E_2$ are defective and that $5\%$ of those produced on $E_3$ are defective. If one tube is picked up at random from a day's production, the probability that it is defective, is

A pair of numbers is picked up randomly (without replacement) from the set $\left[1,2,3,5,7,11,12,13,17,19\right]$. The probability that the number $11$ was picked, given that the sum of the numbers was even, is nearly

The probability that an automobile will be stolen and found within one week is $0.0006$. The probability that an automobile will be stolen, is $0.0015$. The probability that a stolen automobile will be found in one week, is

A bag contains $3$ red and $3$ green balls and a person draws out $3$ at random. He then drops $3$ blue balls into the bag and again draws out $3$ at  random. The chance that the $3$ later balls being all of different colours is

When a missile is fired from a ship, the probability that it is intercepted is $\frac{1}{3}$. The probability that the missile hits the target, given that it is not intercepted, is $\frac{3}{4}$. If three missiles are fired independently from the ship, then the probability that all three hits their targets, is 

There are two bags, one of which contains $3$ black and $4$ white balls, while the other contains $4$ black and $3$ white balls. A die is cast. If the face $1$ or $3$ turns up, a ball is taken from the first bag and if any other face turn up, a ball is chosen from the second bag. The probability of choosing a black ball is