(a) A popular casino game called "Chuck-a-Luck" is played as follows. Gambler's expected net profit in 36 games? Gambler gets his dollar back and, in addition, gets paid $ 35 otherwise, he loses the dollar he bet. The roulette wheel has 38 equally likely numbers. Gambler likes to play American roulette and always bets a dollar on the number 13. Calculate the expected net profit in this game, as an expression involving k. If your number appears on exactly n of the dice, you get your bet back plus you win n įor example, if you bet $ 5 on 3, and the dice show 2,3,3, you get your $ 5 back plus $ 10 winnings, a net profit of $ 10 if the dice show 2,4,6, you lose your bet, a net profit of -$ 5. If your number does not appear on any of the dice, you lose your bet and your net profit is -k dollars. (You decide what k is.) Then three dice are rolled. You place a bet of k dollars and pick a number from 1 through 6. SOLVED: (Expectation and Games, 10 points)
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