3. Three friends A, B, and C are sitting at a table and are playing following game with a fair 6-sided die: A starts throwing the die. If she does not toss number 6, she passes the die forward to B. It is B's turn now, and she throws the die. If B does not toss number 6, she passes the die forward to C. Now, C is throwing. And, again, if C does not throw number 6, she gives the die back to A, and they restart a new round. They continue until the first 6 is thrown, then the game stops. The person who rolled the first 6 is considered the winner. Compute the probability that C wins the game. Hint: You may use the fact that if |g| < 1, then 00 Σ k=0 = - 1 1-9

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