Calculating Probability using Bayes Theorem

Question

I'm trying to calculate using the bayes theorem the exercise below.

But Im confused.

In one company, 40% of the employees are women. Suppose 60% of men workers are married, and 40% of women workers are married. How likely is a married worker to be a man?

What is the correct answer? I found about 0.69.

36/52. that's right?

Answer 1

Indeed:

$P(man|married) = \frac{P(married/man) \cdot P(man)}{P(married/man) \cdot P(man) + P(married/woman) \cdot P(woman)} = \frac{0.6 \cdot 0.6}{0.6 \cdot 0.6 + 0.4 \cdot 0.4}=\frac{9}{13}$

So you are right!

Answer 2

You can also do this with an example. Suppose there are $100$ employees. Then there are $60$ men, $0.6\cdot60=36$ of whom are married, and there are $40$ women, $0.4\cdot40=16$ of whom are married. There are then $36+16=52$ married workers, $36$ of whom are men, so the probability in question is ${36\over52}={9\over13}$.