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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.

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?
 

 

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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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