On the roulette wheel in Las Vegas there are 38 numbered slo

On the roulette wheel in Las Vegas there are 38 numbered slots: numbers 1-36, a zero and a double zero. The numbers 1-36 alternate between red and black. The zero and double zero are green. If you bet on “red” and a red appears on the wheel then you win your bet of $100. If any other color appears (black or green) then you lose your bet of $100. What is the expected value of a $100 bet on “red”?

Solution

Probability of winning a $100 = 18/38

Probability of loosing a $100 = 20/38

expected value = 100 * 18 / 38 + (-100) * 20 / 38

                         = -5.26 dollar