(Answered) Question at the new york state fair in syracuse larry

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Question: At the New York State Fair in Syracuse, Larry encounters a carnival game where for one dollar he may buy a single coupon allowing him to play a guessing game. On each play, Larry has an even chance of winning or losing a coupon. When he runs out of coupons he loses the game. However, if he can collect three coupons, he wins a surprise.

(a) What is the probability Larry will win the surprise?

(b) What is the expected number of plays he needs to win or lose the game.

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