A random number N of dice is thrown. Let A; be the event that N =...

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A random number N of dice is thrown. Let A; be the event that N = i, and assume that P(A₁) = 2−¹, i ≥ 1. The sum of the scores is S. Find the probability that: (a) N = 2 given S = 4; (b) N = 2 given that S = 4 and the first die showed 1; A random number N of dice is thrown. Let A; be the event that N = i, and assume that P(A₁) = 2−¹, i ≥ 1. The sum of the scores is S. Find the probability that: (a) N = 2 given S = 4; (b) N = 2 given that S = 4 and the first die showed 1;