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A random number

*N*of dice is thrown. Let Ai be the event that

*N*= i, and assume that P(Ai) = 1/(2)^i, i >= 1. The sum of the scores is

*S*. Find the probability that:

(a)

*S*= 4, given

*N*is even;

(b) the largest number shown by any die is

*r*, where

*S*is unknown.