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# From the employees of a company ,5 persons are selected to represent them in 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 spokes-person.What is the probability that the spokes-person will be either male or over 35 yr?

$\begin{array}{1 1}(A)\;\large\frac{4}{5}\\(B)\;\large\frac{3}{5}\\(C)\;\large\frac{2}{5}\\(D)\;\large\frac{7}{5}\end{array}$

Toolbox:
• $nC_r=\large\frac{n!}{r!(n-r)!}$
• $P(A\cup B)=P(A)+P(B)-P(A\cap B)$
Step 1:
Let A be the event that selected person is male.
Let B be the event that selected person is over 35yr
$\therefore P(A)=\large\frac{3C_1}{5C_1}=\frac{3}{5}$
$P(B)=\large\frac{2C_1}{5C_1}=\frac{2}{5}$
$P(A \cap B)=\large\frac{1}{5}$
Step 2:
$P\cup B)=P(A)+P(B)-P(A\cap B)$
$\Rightarrow \large\frac{3}{5}+\frac{2}{5}-\frac{1}{5}$
$\Rightarrow \large\frac{5}{5}-\frac{1}{5}$
$\Rightarrow \large\frac{4}{5}$
Hence (A) is the correct answer.