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: 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,$P(E) =\dfrac{3}{5}$ and $P(F) =\dfrac{2}{5}$

Since there is only one male who is over $35$ years of age,
$P(E∩F)=\dfrac{1}{5}$
We know that $P(EUF)=P(E)+P(F)-P(E∩F)$
$∴ P(EUF)=\dfrac{3}{5}+\dfrac{2}{5}-\dfrac{1}{5}=\dfrac{4}{5}$
Thus, the probability that the spokesperson will either be a male or over $35$

years of age is $\dfrac{4}{5}$.