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

##### 1 Answer

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) =

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#1/2# each.

The expected value is obtained as E(X) = 2.#1/2# - 3.#1/2# .

i.e. E(X) = -.5 or loss of $0.5