A high school university entrance examination question:
Players A and B take turns in throwing two dice. The winner is the first player to throw a double six. Player A starts the Game.
Find the probability that Player A wins on the first throw. Attempt: Obviously 1/36.
What is the probability that Player A wins on the first or second throw? Attempt: Probability of win on the second throw is 35/36 times 1/6. Probability of win on first or second throw is therefore the sum of (i) and (ii), or 1/6(1+35/36).
Find the probability that Player A eventually wins the game. Attempt: I tried a geometrical progression using 35/36 as the common ratio, but am stuck. Can you give me a prompt?