Statistics

Question

In the game of roulette a player gives the casino $7 for a bet on the number 5, the player has a 37/38 probability of losing $7 and a 1/38 probability of making a net gain of $245. (The prize is $252 but the players $7 bet is not returned so the net gain is $245.) If a player bets $7 that the outcome is an odd number, the probability of losing $7 is 20/38 and the probability of making a net gain is of $7 is 18/38. (If a player bets $7 on an odd number and wins, the player is given $14 that includes the bet, so the net gain is $7.


a. If a player bets $7 on number 5, what is the player’s expected value?(Round to the nearest cent as needed)
b. The player would expect to lose about? (Round to the nearest cent as needed)

Answer 1

1/36 x 245 - 37/38 x 7 = 245/36 - 259/38 = 6 29/36 - 6 31/38

= 29/36 - 31/38 = 29(38)/36(38) - 31(36)/36(38) = (1102- 1116)/36(38) =-14/36(38)

= -7/18(38) = -7/684 = about -$0.01 = about one cent

or

1/36 x 245 = about 6.80555...

37/38 x 7 = about 6.8158

6.8056- 6.8158 = 0.0102 = about ever slightly more than one penny loss expected