# Total probability law and Bayes

I'm having trouble reasoning this problem:

There's a business that has 3 different offices, "A", "B" and "C". Each one has 50, 75 and 100 employees respectively and 50%, 60% and 70% of the employees of each office are women. The probability that a employee quits his job is the same for women and men.

If you know that a employee (a women) has quit her job, what is the probability that this women has worked in the "C" office?

I know i have to use Bayes somehow, but i don't know how!

Let $O$ be office, $S$ be gender. Then $\Pr(O=A) = 50/225$ $\Pr(O=B)=75/225$ and $\Pr(O=C)= 100/225$
$\Pr(S=W|O=A)=50\%$ $\Pr(S=W|O=B)=60\%$ and $\Pr(S=W|O=C)=75\%$
Then by Bayes $\Pr(O=C|S=W) = \frac{\Pr(O=C)\Pr(S=W|O=C)}{\sum_{x=A,B,C}\Pr(O=x)\Pr(S=W|O=x)} =\frac{ 100/225*75\%} {(100*0.75 +75*0.60 + 50*0.50)/225}$