Question

A group consists of equals number of men and women. Of this group, 20% of the men and 50% of the women are unemployed. If a person is selected at random from this group, the probability of the selected person being employed is

• A. 0.65

Answer 1

The correct option is A 0.65
Let
A = {Employed Person};
$E_1=\left\{\text{Selected Person in Men}\right\}$
$E_2=\left\{\text{Selected Person in Women}\right\}$
By total probability,
$P\left(A\right)=P\left(E_1\right).P\left(A/E_1\right)+P\left(E_2\right).P\left(A/E_2\right)$
$=0.5\times 0.8+0.5\times 0.5$
$=0.4+0.25$
$=0.65$