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Mathematics, 28.02.2021 16:10 trinityine
You play the following simple game of chance. A fair coin is flipped. If it comes up heads, you win a dollar. If it comes up tails, you lose a dollar. Suppose you start with N dollars in your pocket. You play repeatedly until you either reach M dollars or lose all your money, whichever comes first. M and N are fixed positive integers such that 0 < N < M.
a. Show that with probability one the game ends, in other words, that the amount of money in your pocket will eventually hit 0 or M.
b. What is the probability that the game ends with M dollars in your pocket?
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