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There are four men and six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman?

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Solution

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There are four men and six women on the city council.
As one council member is to be selected for a committee at random, the sample space contains $n (S) = (4 + 6) = 10$ elements.
Let $A$ be the event in which the selected council member is a woman
Accordingly $n (A) = 6$
$∴ P (A) = \frac{N u m b e r o f o u t c o m e s f a v o u r a b l e t o A}{T o t a l n u m b e r o f p o s s i b l e o u t c o m e s} = \frac{n (A)}{n (S)} = \frac{6}{10} = \frac{3}{5}$

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