In Shop A, 30 pure ghee and 40 tin adultered ghee are kept for sale while in shop B, 50 pure ghee and 60 tin adultered ghee are there. One tin of ghee is purchased from one of the shops randomly and it is found to be adulterated. Find the probability that it is purchased from shop B.

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Solution

Shop A contains 30 pure ghee container and 40 adultered container
Hence the probability of adultered ghee container is 40/70 = 4/7

Shop B contains 50 pure ghee container and 60 adultered container
Hence the probability of adultered ghee container is 60/110 = 6/11

Probability of choosing a shop is 1/2, as both shop have equal probability of choosing.
So the total probability of adultered ghee will be $\frac{1}{2} \times \frac{4}{7} + \frac{1}{2} \times \frac{6}{11} = \frac{43}{77}$
And the choosing of adultered ghee from shop B is (1/2 )* (6/11) = 6/22

Hence the probability of choosing adultered ghee from shop B is (6/22)/ (43/77) = 21/43

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