Problem 2 (Discrete Random Variable). In a game of American Roulette, a player w

Question

Problem 2 (Discrete Random Variable). In a game of American Roulette, a player will make 20 consecutive bets on the same set of outcomes. She will place her bet on red numbers. Assume each outcomes of each spin are independent and the all outcomes of the roulette wheel are equally likely to occur 29 Figure 1: 38 Possible Outcomes. American Roulette wheel has 2 Green outcomes. 1. What is the probability that the outcome of a single spin will be a red number? 2. What is the probability of winning 6 out of the 20 total bets?

Explanation / Answer

1) P(a single spin will be red number) = Number of red numbers / Total number of outcomes

= 18/38

= 9/19

2) Binomial distribution, P(x) = nCx px qn-x

P(winning 6 out of 20 bets) = 20C6 x (9/19)6 x (10/19)14

= 0.0548

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