Out of 1,000 people in a small town, 500 are members of a choir. Out of these 500 members in a choir, 100 are men. Out of the 50

Question

2 years ago

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Out of 1,000 people in a small town, 500 are members of a choir. Out of these 500 members in a choir, 100 are men. Out of the 50

0 inhabitants that are not in a choir, 300 are men. What is the probability that a randomly drawn man is a member of the choir? Please indicate the probability in a percent.
___ %

Mathematics

2 answers:

Ad libitum [116K] · Answer 1 · 2023-09-12T08:04:28+03:00

Ad libitum [116K]2 years ago

8 0

The correct answer is 25%

-Dominant- [34] · Answer 2 · 2023-09-12T10:17:12+03:00

The probability that a randomly drawn man is a member of the choir is $\boxed{25\% }.$ .

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

$\boxed{{\text{Probability}} = \frac{{{\text{Favorable number of outcome}}}}{{{\text{Total number of outcomes}}}}}$ .

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,

$P\left( {A \cap B} \right) = \dfrac{{100}}{{1000}}$

The probability of event B can be calculated as follows,

$P\left( B \right) = \dfrac{{400}}{{1000}}$

The probability that a randomly drawn man is a member of the choir can be expressed as follows,

$\begin{gathered} {\text{Probability}} = \frac{{P\left( {A \cap B} \right)}}{{P\left( B \right)}} \\ = \frac{{\dfrac{{100}}{{1000}}}}{{\dfrac{{400}}{{1000}}}} \\ = \dfrac{{100}}{{400}} \\ = 0.25 \\ = 25\% \\ \end{gathered}$