Question

In a shop X, 30 tins of pure ghee and 40 tins of adulterated ghee which look alike, are kept for sale while in shop Y, similar 50 tins of pure ghee and 60 tins of adulterated ghee are there. One tin of ghee is purchased from one of the randomly selected shops and is found to be adulterated. Find the probability that it is purchased from shop Y. What measures should be taken to stop adulteration?

Answer 1

Let A be the event that the ghee is adulterated.
Shop X contains 30 pure ghee container and 40 adultered container. 
∴ Probability of adultered ghee container = P(A/X) = \[\frac{40}{70} = \frac{4}{7}\]

Shop Y contains 50 pure ghee container and 60 adultered container. 
∴ Probability of adultered ghee container = P(A/Y) = \[\frac{60}{110} = \frac{6}{11}\]

Also, Probability of choosing a shop is \[\frac{1}{2}\], as both shop have equal probability of choosing., 

P(X) = P(Y) = \[\frac{1}{2}\]

So,
Required Probability, P(Y/A) 

`(P(Y) × P (A/Y))/ (P (X) × P(A/X) + P (Y) × P (A/Y))`

` = (1/2 × 6/11)/(1/2 × 4/7 + 1/2 × 6/11)`

`= (6/11)/((4/7)+(6/11)) = 21/43`

As adulteration is rampant everywhere, consumer should be aware of adulterators and one should take steps to safeguard themselves against those food items.