Question

Alice and Bob play the following game: in each round, Alice first
rolls a single standard fair die. Bob then rolls a single standard fair die. If the difference
between Bob’s roll and Alice’s roll is at most one, Bob wins the round. Otherwise, Alice
wins the round.
(a) What is the probability that Bob wins a single round?
(b) Alice and Bob play until one of them wins three rounds. The first player to
three wins is declared the winner of the series. What is the probability that Bob wins the
series?
(c) In a single series, what is the expected number of wins for Bob?

Answer 1

Answer:

You have not stated that A's die is 1-12 (on the faces) and B's 1-20 and both are fair dice. Obviously there is no hope of approaching this question if we know nothing about the dice. Or to be more accurate, the reasoning will be totally different.

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