# 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?

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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.

Complete step-by-step answer:

It is given that there are 4 men and 6 women on the city council.

Therefore there are (4 + 6) =10 members on the city council.

Therefore out of 10 the number of ways of selecting one council member for a committee at random is${}^{10}{C_1}$.

Now we have to find out how likely it is that it is a woman.

So, there are 6 women therefore out of 6 the number of ways to select one woman for the committee is${}^6{C_1}$.

So, the probability (P) that it is a woman is the ratio of favorable number of outcomes to the total number of outcomes.

${\text{P = }}\dfrac{{{\text{favorable outcome}}}}{{{\text{total possible outcome}}}}$

Therefore the probability that it is a women is

$p = \dfrac{{{}^6{C_1}}}{{{}^{10}{C_1}}} = \dfrac{6}{{10}} = \dfrac{3}{5}$.

So, this is the required probability that it is a woman.

So, this is the required answer.

Note – Whenever we face such types of problems the key concept is simply to take into consideration ways of linking the combination concepts with that of probability. The gist of total favorable cases and the total number of cases will help you get on the right track to get the answer.

Complete step-by-step answer:

It is given that there are 4 men and 6 women on the city council.

Therefore there are (4 + 6) =10 members on the city council.

Therefore out of 10 the number of ways of selecting one council member for a committee at random is${}^{10}{C_1}$.

Now we have to find out how likely it is that it is a woman.

So, there are 6 women therefore out of 6 the number of ways to select one woman for the committee is${}^6{C_1}$.

So, the probability (P) that it is a woman is the ratio of favorable number of outcomes to the total number of outcomes.

${\text{P = }}\dfrac{{{\text{favorable outcome}}}}{{{\text{total possible outcome}}}}$

Therefore the probability that it is a women is

$p = \dfrac{{{}^6{C_1}}}{{{}^{10}{C_1}}} = \dfrac{6}{{10}} = \dfrac{3}{5}$.

So, this is the required probability that it is a woman.

So, this is the required answer.

Note – Whenever we face such types of problems the key concept is simply to take into consideration ways of linking the combination concepts with that of probability. The gist of total favorable cases and the total number of cases will help you get on the right track to get the answer.

Last updated date: 22nd Sep 2023

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