Question

2. An American roulette wheel contains 38 numbers: 18 are red, 18 are black, and 2 are green. When the roulette wheel is spun, the ball is equally likely to land on any of the 38 numbers. Suppose that you bet $1 on red. If the ball lands on a red number, you win $1; otherwise you lose your $1. Let X be the amount you win on your $1 bet.

Answer 1

are red, From the provide information, the total number wheel contains are 38 in which 18 18 are black and 2 are green. Profanility of getting a red number Pened )= 18 0.474. 38 ll other than red) = 20 38 (b Expected ualue E(X)= $1 X 0.474 + (- $160.526) 0-474 0.526 - $0.0 52 "So the is = $-0.052, 0.526 expected value the long ſ40 a بما 16 we Expected value indicates what will happen in every time that we bet & lon red. While might win several time in in the short term, in the long run will loge over 5 cents on average .each time that we play. (c) In 100 dimes a expected value to lose 100x (-0.052)=$5.2 con 1000 times expected value to lose 1000 X (0.052) $52. @. Since in this game in long run there a chace losing is are more than the hace of winni Therefore This is 영 not a fair game.