# Probability - coin toss

Al, Bob and Carlos are playing a silly game. Al flips a coin. If he gets heads, the game ends and he wins. If not, Bob flips the coin. If he gets heads, the game ends and he wins. If not, Carlos flips the coin. If he gets heads, the game ends and he wins. If not, the coin is returned to Al and the process begins again. The game continues until someone gets heads. What is the probability of each of them winning?

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#### Solution Preview

First, let's consider the probability Al will win the game.

If Al wins the game, then he will get a head at the 1st turn, or at the 4th turn, or at the 7th turn, ..., or at the (3k+1)th turn, ..., where k=0,1,.... But if he get a head at the (3k+1)th ...

#### Solution Summary

This is a probability problem regarding a coin toss game.

$2.19