10. Starting with Hillary, two players, Hillary and Donald, take turns and roll a fair die. The one who rolls a 6 first is the winner. What is the probability that Hillary will win?

Hint: For i ≥ 1, let Ai be the event that the first 6 is rolled on Hillary’s ith turn. Let H be the event that Hillary will win. Write P(H) in terms of P(Ai)’s. Note that for 

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|r| < 1, m 1, im r = 1/(1 r).