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An urn contains 2 white and 2 black balls. A ball is drawn at random. If it is white, it is not replaced into the urn. Otherwise, it is replaced with another ball of the same colour. The process is repeated. Find the probability that the third ball drawn is black.

An urn contains 2 white and 2 black balls. A ball is drawn at random. If it is white, it is not replaced into the urn. Otherwise, it is replaced with another ball of the same colour. The process is repeated. Find the probability that the third  ball drawn is black.

Grade:12

1 Answers

denesh
23 Points
9 years ago
3/4-(case 1:(1/2*1/3*1+1/2*2/3*3/4) + case 2:(1/2*2/5*2/3+1/2*3/5*2/3))
This has to be solved by taking cases..
Case 1 is drawing a white in first attempt and 2 is for drawing a black (it is one in the 3rd term of case 1 first expression bcz by then all white balls would have gone and so on for the next sub cases that arise..

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