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There are 4 men and 6 women on the city council. If one council member is selected for a committee at random, how likely is that it is a woman?

Last updated date: 27th Mar 2023
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Hint – In this question the number of men and women is given and we need to choose one person. So we need to find the probability that the chosen person is a woman. Now first find ways of selecting one person out of total people that is 10, then find the ways of choosing 1 woman out of the total number of women. Then using the basic definition of probability we can get the answer.

Therefore out of 10 the number of ways of selecting one council member for a committee at random is${}^{10}{C_1}$.
So, there are 6 women therefore out of 6 the number of ways to select one woman for the committee is${}^6{C_1}$.
${\text{P = }}\dfrac{{{\text{favorable outcome}}}}{{{\text{total possible outcome}}}}$
$p = \dfrac{{{}^6{C_1}}}{{{}^{10}{C_1}}} = \dfrac{6}{{10}} = \dfrac{3}{5}$.