Suppose that aquarium a contains 4 yellow fishes and 3 black fishes.Aquarium b c

Question

Suppose that aquarium a contains 4 yellow fishes and 3 black fishes.Aquarium b contains 3 yellow and 11 black fishes. Let me play an easy game. If i arbitrarily win, we pick a fish from aquarium a; if i arbitrarily lose, we pick a fish from aquairium b. a) What is the probability that a yellow fish is picked? b) What is P[Y|A], the conditional probability that a yellow fish was picked given that we picked the fish from aquarium a? c) What is P[A|B], the conditional probability the fish was picked from aquarium a given that a black fish was picked?

Explanation / Answer

a) Probability of winning = Probability of losing = 1/2

Probability that a yellow fish is picked from a = 4/7

Probability that a yellow fish is picked from b = 3/14

=> Probability of picking a yellow fish = 1/2 * 4/7 + 1/2 * 3/14 = 0.3929.

b) There are 4 yellow fishes in a out of 7.

=> P(Y|A) = 4/7 = 0.5714

c) Probability of picking from a given that it is a black fish = 1/2 * 3/7 + 1/2 * 11/14

=> P(A|B) = (1/2*3/7) / (1/2 * 3/7 + 1/2 * 11/14) = 0.3529.

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