Question

A player pays $1.50 to play the following game: He tosses two fair coins and receives $1 if he tosses no heads, $2 if he tosses one head, and $3 if he tosses two heads. Find the player’s expected value for this game.

Answer 1

The expected value formula is

$E(X)=\Sigma X_ip_i$

So, we have to find the probability of each event.

In this case, heads and tales have the same probability of 1/2.

Tossing no head has a probability of 1/2.

Tossing one head has a probability of 1/2.

Tossing two heads have a probability of 1/4.

Now, we multiply each event by its value, then we sum

$E(X)=1\cdot\frac{1}{2}+2\cdot\frac{1}{2}+3\cdot\frac{1}{4}=\frac{1}{2}+1+\frac{3}{4}=2.25$

Hence, the expected value is $2.25.