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An urn B1 contains 2 white and 3 black chips and another urn B2 contains 3 white and 4 black chips. One urn is selected at random and a chip is drawn from it. If the chip drawn is found black, find the probability that the urn chosen was B1.

An urn B1 contains 2 white and 3 black chips and another urn B2 contains 3 white and 4 black chips. One urn is selected at random and a chip is drawn from it. If the chip drawn is found black, find the probability that the urn chosen was B1. Correct Answer 21⁄41

Let E1, E2 denote the vents of selecting urns B1 and B2 respectively. Then P(E1) = P(E2) = 1⁄2 Let B denote the event that the chip chosen from the selected urn is black . Then we have to find P(E1 /B). By hypothesis P(B /E1) = 3⁄5 and P(B /E2) = 4⁄7 By Bayes theorem P(E1 /B) = (P(E1)*P(B│E1))/((P(E1) * P(B│E1)+P(E2) * P(B│E2)) ) = ((1/2) * (3/5))/((1/2) * (3/5)+(1/2)*(4/7) ) = 21/41.

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