A and B flip coins starts and continues flipping until a tail occurs, at which point starts flipping and continues until there is a tail Then takes over, and so on Let P 1 be the probability of the coin landing on heads when flips and P 2 when flips The winner of the game is the first one to get a ...

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A and B flip coins. starts and continues flipping until a tail occurs, at which point starts

Question:

A and B flip coins. starts and continues flipping until a tail occurs, at which point starts flipping and continues until there is a tail. Then takes over, and so on. Let P₁ be the probability of the coin landing on heads when flips and P₂ when flips. The winner of the game is the first one to get

a. 2 heads in a row;

b. a total of 2 heads;

c. 3 heads in a row;

d. a total of 3 heads.

In each case, find the probability that wins.

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