Question

A player tosses two fair coins. He wins $5 if 2 heads occur, $2 if 1head occurs and $1 if no heads occur. (i) Find his expected winnings. (ii) How much should he pay to play the game if it is to be fair?

Answer 1

In case of a player tosses two fair coins then following events will occur:

S = [HT, TH, TT, HH]

(i) Expected winnings

$Expected-gain = \Sigma X_i P(X_i )$

$=(5\times\frac{1}{4})+(2\times\frac{1}{2})+(1\times\frac{1}{4})$

$=\frac{5}{4}+1+\frac{1}{4}=\frac{10}{4}=2.5$

(ii) Required pay to play the game

The player should pay exactly $2.5 if he wants to be fair in the game. It is because if he will pay less than $2.5 then the game is favorable to him, while unfavorable in case of pay more than.