Question

A player tosses two fair coins. He wins $ 2 if 2 head occur and $1 if 1 head occur. On the other hand, he loses $3 ıf no head occurs. Determine the player's expected value and if the game is favorable to the player.

Answer 1

There are 2 coins hence the sample space will be 4.

(HH, HT, TH, TT)

2 heads occurs once, 1 head occurs twice and no head appears once.

Expectation =$\sum x_i p_i$

=$2*\frac 1 4+1*\frac 2 4+(-3)*\frac 1 4$

=0.25

The game is favorable to the player since the expected value is positive.