Question

Two brothers, Max and Sam, take turns at trying to win a prize. Max, being the younger, goes first, and Sam goes second. If no one wins on their first attempt, this process is repeated until someone wins. For Max to win, he must roll a die for a 5 or a 6. For Sam to win, he must toss a coin heads. What is the probability that Max wins?

Answer 1

P(Max win in any attempt) = 2/6 = 1/3

P(Sam win in any attempt) = 1/2

P(Max loose in any attempt) = 2/3

P(Same loose in any attempt = 1/2

Max win will follows an infinte geometric sequence where it will go like (WL, LLW, LLLLW, ....) and so one. L -> player losing in his turn. W --> player wining in his turn.

This is infinite geometric series with a = 1/3 and r = 1/3

Hence, 1/2 or 0.5 is the probability that Max will win.