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Question
One urn contains two black balls (labelled B1 and B2) and one white ball. A second urn contains one black ball and two white balls (labelled W1 and W2). Suppose the following experiment is performed. One of the two urns is chosen at random. Next a ball is randomly chosen from the urn. Then a second ball is chosen at random from the same urn without replacing the first ball. What is the probability that two black balls are chosen?
Solution
Given that one of the two urns is choosen
Then a ball is randomly choosen from the urn
Then a second ball is choosen at random from the same urn without replacing the first ball
If two black balls are choosen
Then the favourable events are B1B2, B2B1
i.e. 2
∴ Required probability = `2/12 = 1/6`
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