# What is the expected value of a coin toss game where you win $2 for each heads and lose$3 for each tails?

Nov 3, 2015

The explanation below is based on the assumption that a fair coin is tossed.

#### Explanation:

When a fair coin is tossed, p(H) = $\frac{1}{2}$ and p(T) =$\frac{1}{2}$.

For getting a head, the winning is $2 and for a tail, the loss is$3.
So X is a random variable that takes values 2 or -3.with probability $\frac{1}{2}$ each.
The expected value is obtained as E(X) = 2.$\frac{1}{2}$ - 3.$\frac{1}{2}$.
i.e. E(X) = -.5 or loss of \$0.5