Question

In a game, a person is paid Rs. 5 if he gets all heads or all tails when three coins are tossed, and he will pay Rs. 3 if either one or two heads show. What can he expect to win on the average per game ?

Answer 1

Let X be the amount received by the person. Then, X can take values 5 and -3 such that

P( X = 5) = Probability of getting all heads or all tails when three coins are tossed

P( X = 5) = $\frac{2}{8}=\frac{1}{4}$

P( X = -3) = Probability of getting one or two heads

P(X = -3) = $\frac{6}{8}=\frac{3}{4}$

Therefore, expected amount to win, on the average, per game

$=\overline{X}=\sum p_i{x}_i=5\times \frac{1}{4}+-3\times \frac{3}{4}=-1$

Thus, the person will, on average, lose Rs. 1 per toss of the coins.