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Two friends, Louie and Duke, take turns at trying to win a prize. Louie goes first,...

Two friends, Louie and Duke, take turns at trying to win a prize. Louie goes first, Duke second. If no one wins on their first attempt, Louie goes again, then Duke, etc. For Louie to win, he must toss 3 coins and have them all land heads. For Duke to win, he must select a card at random from a standard deck and have it be a heart. What are their respective probabilities of winning?

Math   Statistics-And-Probability   
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Answer #1

Probability of Louie to win on single attempt, pLW = (1/2)^3 = 1/8

Probability of Louie to lose on single attempt pLL = 1 - 1/8 = 7/8

Probability of Duke to win on single attempt, pDW = 13/52 = 1/4

Probability of Duke to lose on single attempt, pDL = 1 - 1/4 = 3/4

Probability of Louie to win on kth attempt =

Probability of Louie to win is,

(By Sum of infinite geometric series)

Probability of Duke to win is,

= 1 - Probability of Louie to win

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