SOLUTION: A town has a population of 10,000 consisting of 6000 males and 4000 females. Out of these 300 males are employed and 400 females are employed. Find a probability that an employed

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Question 883981: A town has a population of 10,000 consisting of 6000 males and 4000 females. Out of these 300
males are employed and 400 females are employed. Find a probability that an employed person
chosen at random is female.
Answer by Theo(13342) About Me  (Show Source):
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there are 700 employed persons of which 300 are male and 400 are female so, given that the person is employed, the probability that the person is female is 400/700 which is equal to 4/7.

the formula used to derive this is:

p(female given employed) = p(employed and female) / p(employed)

since probability tbat the person is employed is equal to 700 / 10000 and probobability that the person is employed and female at the same time is 400 / 10000, this formula becomes:

p(female given employed) = (400 / 10000) / (700 / 10000) which is equal to (400 / 10000) * (10000 / 700) which is equal to 400 / 700 which is equal to 4/7.