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You and your opponent both roll a fair die. If you both roll the same number,...

You and your opponent both roll a fair die. If you both roll the same number, the game is repeated, otherwise whoever rolls the larger number wins. Let N be the number of times the two dice have to be rolled before the game is decided. (d) Assume that you get paid $10 for winning in the first round, $1 for winning in any other round, and nothing otherwise. Compute your expected winnings.

Answer:

(d) You get paid $10 with probability 5/12 , $1 with probability 1/12 , and 0 otherwise, so your

expected winnings are 51/12.

The answer is there but I don't understand how you get the probability.

Why is the probability 5/12 for winning in the first round? and why is the probability 1/12 for winning in any other round?

math   Statistics-And-Probability   
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