Question

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 500 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 as a percent

Answer 1

Answer:

The key is figuring out how many of the 1000 people are men. Then you can use that number to find the answer based on how many men are in the choir vs the total male population of the town.

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We know that out of the 500 people who are not in choir, 300 are men.

We also know that 100 men are in the Choir.

That means there are a total of 400 men in this small town, and 600 women in the town.

Out of the 400 men, 100 are in the choir.  So, if you randomly poll one of the 400 men in the town, you have a 1 in 4 chance that man is in the Choir.  

1 in 4 = A 25% probability.

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Step-by-step explanation:

Answer 2

probability that a randomly drawn man is a member of the choir is 1/4 that is 25%

Step-by-step explanation:

given that the total number of people in the town is 1000

number of people in choir,C= number of inhabitants,I =500

number of men(M) in choir=100

number of men in inhabitants =300

then,

p(C)= p(I)=½

p(men and in choir)= ⅕

p(men and in inhabitants)= ⅗

$p(m) = \frac{300 + 100}{1000} = \frac{4}{10}$

then p(given a man is chosen and he is from choir)

$p(C|M)= \frac{p(c \: n \: m)}{p(m)} = \frac{ \frac{1}{2} \times \frac{1}{5} }{ \frac{4}{10} } \\ = \frac{1}{10} \times \frac{10}{4} = \frac{1}{4}$

probability that a randomly drawn man is a member of the choir is 1/4 that is 25%

DEFINITIONS AND IMPORTANT CONCEPTS TO KNOW

CONDITIONAL PROBABILITY

It is the probability of happening an event such that some event has already happened.

$p(a|b) = \frac{p(a \: n \: b}{p(b)}$

were ,event has given that aldready happened

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