8. From the employees of a company, $\small 5$ 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 $\small 35$ years?

H Harsh Kankaria

Given,

Total number of persons = 5

No. of male spokesperson  = 3

No. of spokesperson who is over 35 years of age = 2

Let E be the event that the spokesperson is a male and F be the event that the spokesperson is over 35 years of age.

$\therefore$  $P(E) = \frac{3}{5}\ and\ P(F) = \frac{2}{5}$

Since only one male is over 35 years of age,

$\therefore$ $P(E\cap F) = \frac{1}{5}$

We know,

$P(E \cup F) = P(E) + P(F) - P(E \cap F)$

$\implies P(E \cup F) = \frac{3}{5} + \frac{2}{5} - \frac{1}{5} = \frac{4}{5}$

Therefore, the probability that the spokesperson will either be a male or over 35 years of age is $\frac{4}{5}$.

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