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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. The process is repeated. Find the probability that th

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. The process is repeated. Find the probability that the third ball drawn is black

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P(W)=\frac{2}{4}=\frac{1}{2}, \quad P(B)=\frac{1}{2}

 

P(3 rd \text { black })=\frac{1}{6} \times 1+\frac{1}{3} \times \frac{2}{3}+\frac{1}{4} \times \frac{2}{3}+\frac{1}{4} \times \frac{1}{2}=\frac{49}{72}

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Divya Sharma

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