A player can \"bet on a line\" by placing a chip at location A in the figure to

Question

A player can "bet on a line" by placing a chip at location A in the figure to the right. By placing the chip at A, the player is betting on 1, 2, 3, 0 and 00. This bet pays 5.5 to 1, which means that if a player wins, the player wins 5.5 dollars as well as keeping his or her bet. When the player loses, he or she loses $1. Recall that there are 38 numbers on a roulette wheel. Determine the expected value of betting on the roulette wheel. The expected value of betting on the roulette wheel is $ (Round to the nearest cent as needed.)

Explanation / Answer

Since there are 38 numbers on a roulette wheel, the probability of a player winning is 5/38 and the probability of the player losing is 33/38. Then, the expected value of a player betting on the roulette wheel is as under:

Expected value is calculated as follows:

[(probability of winning)(amount won per bet) - (probability of losing)(amount lost per bet)] =                            [5/38*(5.5) – (33/38)*1] = (27.5/38) – 33/38 = - 5.5/38 = - 0.144736842

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