Amit M Agarwal Solutions for Chapter: Advanced Probability, Exercise 1: Work Book Exercise 16.1

A bag contains $n$ white and $n$ black balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each pair consists of one white and one black ball, is

If $X$ speaks truth in $60\%$ and $Y$ in $50\%$ of the cases, then, the probability that they contradict each other narrating the same incident, is

If the probability of hitting a target by three marksmen are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$. Then, the probability that one and only one of them will hit the target when they fire simultaneously, is

From an urn containing six balls,$3$ white and $3$ black ones, a person selects at random an even number of balls (all the different ways of drawing an even number of balls are considered equally probable, irrespective of their number). Then, the probability that there will be the same number of black and white balls among them, is

One purse contains $6$ copper coins and $1$ silver coin; a second purse contains $4$ copper coins. Five coins are drawn from the first purse and put into the second and then $2$ coins are drawn from the second and put into the first. The probability that the silver coin is in the second purse, is

Fifteen coupon are numbered $1, 2, \dots ,15$, respectively. Seven coupons are selected at random one any time with replacement. The probability that the largest number appearing on a selected coupon is $9$, is

A pack of playing cards was found to contain only $51$ cards. If the first $13$ cards which are examined, are all red, then the probability that the missing card is black, is

In a bag, there are three tickets numbered $1,2,3$. A ticket is drawn at random and put back and this is done four times. The probability that the sum of the numbers is even, is