A roulette wheel has the numbers 1 through 36, 0, and 00. A bet on three numbers pays 11 to 1 (that is, if you bet $1 and one of the three numbers you bet comes up, you get back your $1 plus another $11). How much do you expect to win with a $1 bet on three numbers?

Answer:You are expected to lose $0.05 (or win -$0.05)Step-by-step explanation:Since the roulette wheel has the numbers 1 through 36, 0, and 00, there are 38 possible outcomes.In this bet, you are allowed to pick 3 out of the 38 numbers. Thus, your chances of winning (P(W)) and losing (P(L)) are:[tex]P(W)=\frac{3}{38}\\P(L) = 1 - P(W)\\P(L) = \frac{35}{38}\\[/tex]The expected value of the bet is given by the sum of the product of each outcome pay by its probability. Winning the bet means winning $11 while losing the bet means losing $1. The expected value is:[tex]EV = (11*\frac{3}{38}) -(1*\frac{35}{38})\\EV = -\$0.0525[/tex]Therefore, with a $1 bet, you are expected to lose roughly $0.05