Chapter 4.1, Problem 37E

Finding an Expected Value In Exercises 37and 38, find the expected value E(x) to the player for one play of the game. If x is the gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose.

37. In American roulette, the wheel has the 38 numbers, 00, 0, 1, 2, …, 34, 35, and 36, marked on equally spaced slots. If a player bets $1 on a number and wins, then the player keeps the dollar and receives an additional $35. Otherwise, the dollar is lost.