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. $2/3$

Answer 1

The correct option is B $3/8$

We have,

Probability that the people have brown hair

$P\left(A\right)=\frac{40}{100},$

Probability that the people have brown eyes
$P\left(B\right)=\frac{25}{100}$ and

Probability that the people have both brown hair and brown eyes

$P(A\cap B)=\frac{15}{100}$

So, required probability

$P\left(\frac{B}{A}\right)=\frac{P(A\cap B)}{P\left(A\right)}=\frac{15/100}{40/100}=\frac{3}{8}$