Question

In a class there are $10$ men and $20$ women. Out of them half of the number of men and half of the number of women have brown eyes. Out of them if a person is chosen at random, the chance that for the person chosen to be a man or brown eyed person is

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{3}{4}$
• D. $\frac{1}{4}$

Answer 1

The correct option is B $\frac{2}{3}$

Let,
$A=$ chosen person is a man
$B=$ chosen person has brown eyes
$P\left(A\right)=\frac{10}{30},P\left(B\right)=\frac{15}{30},P(A\cap B)=\frac{5}{30}$
$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$\Rightarrow P(A\cup B)=\frac{10}{30}+\frac{15}{30}-\frac{5}{30}=\frac{2}{3}$