Question

In a shop X, 30 tins of ghee of type A and 40 tins of ghee of type B which look alike, are kept for sale. While in shop Y, similar 50 tins of ghee of type A and 60 tins of ghee of type B are there. One tin of ghee is purchased from one of the randomly selected shop and is found to be of type B. Find the probability that it is purchased from shop Y.

Answer 1

Suppose A: Getting type B ghee

E₁: Ghee purchased from X

E₂: Ghee purchased from Y

∴ `P(E_1) = 1/2` and `P(E_2) = 1/2`

Now, `P(A/E_1) = 40/70 = 4/7`

`P(A/E_2) = 60/110 = 6/11`

From Bayes’ Theorem

`P(E_2/A) = (P(E_2)P(A//E_2))/(P(E_1)P(A//E_1) + P(E_2)P(A//E_2)`

`P(E_2/A) = (1/2 xx 6/11)/(1/2 xx 4/7 + 1/2 xx 6/11)`

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

= `42/86`

Therefore, `P(E_2/A) = 21/43`.