Question: Alice, Bob and Cathy take turns at rolling a 6-sided die, in that order. The first player to roll a 6 wins the game. After

Alice, Bob and Cathy take turns at rolling a 6-sided die, in that order. The first player to roll a 6 wins the game. After that, the remaining two players keep rolling (in order) and the first among the two to roll a 6 is deemed to come second and the other player comes last.

(a) What is the probability that Alice wins?

(b) Given that Alice wins, what is the probability that Bob comes second?

(c) Given that Bob comes second, what is the probability that Cathy wins?

(d) What is the expected number of die rolls by Bob?

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