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alexgriva [62]
4 years ago
9

An urn contains one white chip and a second chip that is equally likely to be white or black. A chip is drawn at random and retu

rned to the urn. Then a second chip is drawn.What is the probability that a white appears on the second draw given that a white appeared on the first draw? (Hint: Let Wi be the event that a white chip is selected on the ith draw, i = 1, 2. Then P(W2|W1) = P(W1∩W2) P(W1) . If both chips in the urn are white, P(W1) = 1; otherwise, P(W1) = 1/2)
Mathematics
1 answer:
forsale [732]4 years ago
8 0

Answer:

P(W_{2} | W_{1}) = 1 if both chips are white, P(W_{2} | W_{1}) = 1/2 otherwise

Step-by-step explanation:

W_{i} represents the event that a white chip is selected on the ith draw. Then P(W_{2} | W_{1}) = P(W_{2}\cap W_{1})/P(W_{1}). If both chips in the urn are white, P(W_{2}\cap W_{1}) = 1 and P(W_{1}) = 1, then P(W_{2} | W_{1}) = P(W_{2}\cap W_{1})/P(W_{1}) = 1. If one chip is white and the other is black, then P(W_{2} | W_{1}) = P(W_{2}\cap W_{1})/P(W_{1}) = P(W_{2})P(W_{1})/P(W_{1}) = P(W_{2}) = 1/2 because the event a white chip is selected on the first draw is independent from the event  a white chip is selected on the second draw, and because the chips are drawn at random.

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