Question

Jim loves to play roulette! He bets $10 on a single number, usually the number 13. He has a 138 chance of winning. If the ball lands on his number, he wins $350 (and gets to keep his $10 bet!). If it lands on any other number, a 37/38 probability, he loses his bet. What is the expected value of a game of roulette?Round to the nearest cent. Do not round until your final answer.

Answer 1

We can calculate the expected value of the game by means of the following formula:

Expected value = P(A)×money he wins + P(~A)×(-money he bets)

Where A is an event, in this case, the event is the ball lans on 13 and ~A implies that this event is not happening.

In this case, P(A) equals 1/38, since there is only a slot with 13 and there are 38 slots in total. The money he wins equals $350, P(~A) equals 37/38 and the money he bets equals $10. By replacing these values into the above equation, we get:

Expected value = 1/38×35 + 37/38×(-10) = -0.53

Then, the expected value of this game equals -0.53