Need help with Probability

Mathematics
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Apple found that 30% of their employees were International and 70% were Domestic. Further, of their International employees, 25% were male. Of their Domestic employees, 60% were male. Given that an Apple employee is female, what is the probability that she is a Domestic employee?

Mar 30th, 2015

We can set up a table. There are four possibilities:

Male / Domestic

Male / International

Female / Domestic

Female / International

So we have that P(I) = 0.3, and P(D) = 0.7.

Since 25% of the international employees were male, P(F and I) = 75% x P(I), so P(F and I) = 3/4 x 0.30 = 0.225

Similarly, Since 60% of the domestic employees were male, P(F and D) = 40% x P(D), so P(F and D) = 0.4 x 0.70 = 0.28

So P(D | F) = P(F and D)/(P(F and D) + P(F and I) )

= 0.28 / (0.28 + 0.225)

= 0.5546


Mar 30th, 2015

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