Question

From the employees of a company $5$ persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows:

S.No	Name	Sex	Age in years
1	Harish	M	30
2	Rohan	M	33
3	Sheetal	F	46
4	Alis	F	28
5	Salim	M	41

A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over $35$ years?

Answer 1

Let $E$ be the event in which the spokesperson will be a male and $F$ be the event in which the spokesperson will be over $35$ years of age.
Accordingly $P\left(E\right)=\frac{3}{5}$ and $P\left(F\right)=\frac{2}{5}$ Also $P(E\cap F)=\frac{1}{5}$
We know that $P(E\cup F)=P\left(E\right)+P\left(F\right)-P(E\cap F)$
$\therefore P(E\cup F)=\frac{3}{5}+\frac{2}{5}-\frac{1}{5}=\frac{4}{5}$
Thus the probability that the spokesperson will either be a male or over $35$ years of age is $\frac{4}{5}$