Question

A roullette wheel used in a US casino has 38 slots, of which18 are red, 18 are black, and 2 are green. A roulette wheelused in a French casino has 37 slots, of which 18 are red, 18 areblack and 1 is green. A ball is rolled around the wheel andends up in one of the slots with equal probability. Supposethat a player bets on red. If a $1 bet is placed, the player wins$1 if the ball ends up in a red slot. (The player's $1 bet isreturned). If the ball ends upin a black or green slot, theplayer loses $1. Find the expected value of this game to theplayer in

(a) The United States.
(b) France

Answer 1

In the US casino, the expected value of the game is $0.474 and in the French casino it is $0.486.

Step-by-step explanation:

Expected Value in US:

In the US casino, there are 18 red slots out of 38. Since the probability of winning is equal to the number of red slots divided by the total number of slots, the probability of winning is 18/38. The player wins $1 if the ball ends up in a red slot, so the expected value can be calculated by multiplying the probability of winning by the amount won, and subtracting the probability of losing times the amount lost:

Expected Value = (18/38) * $1 + (20/38) * (-$1) = $0.474

Expected Value in France:

In the French casino, there are 18 red slots out of 37. Using the same formula, the expected value can be calculated as:

Expected Value = (18/37) * $1 + (19/37) * (-$1) = $0.486