# Suppose that 5 men out of 100 and 25 women out of 1000 are good orators. Assuming that there are equal number of men and women, find the probability of choosing a good orator.

$E_{1}: Choosing a man$

$P(E_{1}) = \frac{1}{2}$

$E_{2}: Choosing a woman$

$P(E_{2}) = \frac{1}{2}$

$A: Choosing a good orator$

$P(\frac{A}{E_{1}} )=\frac{5}{100}=\frac{1}{20}$

$P(\frac{A}{E_{2}} )=\frac{25}{1000}=\frac{1}{40}$

$\\ P(A)=P(\frac{A}{E_{1}} ) P(E_{1})+P(\frac{A}{E_{2}} ) P(E_{2}) \\\\ =\frac{1}{20} \times \frac{1}{2}+\frac{1}{40} \times \frac{1}{2} \\\\=\frac{3}{80}$

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