# In a certain town, 40% of the people have brown hair, 25% have brown eyes and 15% have both brown hair and brown eyes. If a person selected at random from the town, has brown hair, the probability that he also has brown eyes is

Question : In a certain town, 40% of the people have brown hair, 25% have brown eyes and 15% have both brown hair and brown eyes. If a person selected at random from the town, has brown hair, the probability that he also has brown eyes is

(A) 1/5

(B) 3/8

(C) 1/3

(D) 2/3

We have, $P\left( A\right) =\dfrac{40}{100},P\left( B\right) =\dfrac{25}{100},andP\left( A\cap B\right) =\dfrac{15}{100}$
So, $P\left( B| A\right) =\dfrac{P\left( A\cap B\right) }{P\left( A\right) }=\dfrac{\dfrac{15}{100}}{\dfrac{40}{100}}=\dfrac{3}{8}$.