The probability that a randomly drawn man is a member of the choir is [tex]\boxed{25\% }.[/tex].
Further explanation:
The probability is the chance of any event.
The probability can be obtained as the ratio of favorable number of outcomes to the total number of outcomes
[tex]\boxed{{\text{Probability}} = \frac{{{\text{Favorable number of outcome}}}}{{{\text{Total number of outcomes}}}}}[/tex].
Given:
There are 1000 people in a small town, 500 are members of choir. Out of which 100 are men.
There are 500 inhabitants that are not in a choir.
Explanation:
There are total 1000 members.
The number of men that are member of choir is 100.
There are 500 members in a choir and 100 members are men.
The total number of man is 300 + 100 = 400.
Consider an event A man is a member of choir.
Consider an event B that man is randomly selected.
The probability of event A can be calculated as follows,
[tex]P\left( {A \cap B} \right) = \dfrac{{100}}{{1000}}[/tex]
The probability of event B can be calculated as follows,
[tex]P\left( B \right) = \dfrac{{400}}{{1000}}[/tex]
The probability that a randomly drawn man is a member of the choir can be expressed as follows,
[tex]\begin{gathered} {\text{Probability}} = \frac{{P\left( {A \cap B} \right)}}{{P\left( B \right)}} \\ = \frac{{\dfrac{{100}}{{1000}}}}{{\dfrac{{400}}{{1000}}}} \\ = \dfrac{{100}}{{400}} \\ = 0.25 \\ = 25\% \\ \end{gathered}[/tex]
The probability that a randomly drawn man is a member of the choir is [tex]\boxed{25\% }[/tex].
Learn more:
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Probability
Keywords: small town, inhabitants, member, choir, 500 members, randomly, probability, man, 1000 people, 100 men.
