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The following two-stage random experiment is performed: Firstly, a fair die is rolled, which will show a number i ∈ {1,2,3,4,5,6} each with probability 1/6. After this, i red balls and (6-i) black balls are placed into an urn, shuffled, and five balls are randomly drawn from this urn.
(a) Let Ai be the event "an i is rolled" and B the event "five red balls are drawn". Compute the conditional probabilities P(B|Ai) for i ∈ {1,2,3,4,5,6}.
(b) Determine P(B)
(c) Given that all five drawn balls are red, what is the probability that a "six" was rolled?
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