3. Mr. Z is in a casino for the first time! He decides to play some American rou

Question

3. Mr. Z is in a casino for the first time! He decides to play some American roulette. First, he bets $1 on red and he wins! Then, he bets $1 on red again and he wins again! Use this information to answer the following questions.

paste your output along with an explanation.

Note that this is American roulette with 38 slots: 18 red, 18 black, and 2 green.

(4 points)

A. If Mr. Z plays a third round and bets $1 on red, what is the probability that he will win this time? Show calculations.

B. If an individual plays three rounds of American roulette, what is the probability that he or she will win all three times? Show calculations.

C. Let X denote your winnings (winnings only) each time you place a $1 bet on red with a $2 payout if you win.     State the probability distribution of X.

D. Calculate the expected gain or loss on a $1 bet on red given a payout of $2 if you win. You need to calculate your expected winnings and then deduct the cost to play.   Show calculations.

Explanation / Answer

A) As third win is independent of first two prob for winning = no of red/total = 18/38 = 0.4737

B) X no of wins is binomial with p = 0.4737 and n =3

P(X=3) = 0.47373 = 0.1063

-------------------------------------------

C) Each time pay = 1 if win pay out =2

Then X can be -1          1

P(X)                  0.5263    0.4737

xP(x)                -0.5263    0.4737

Expected gain = 0.0526

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