I need some help with this stats question. I thought the answer was 1/3 by Bayes

Question

I need some help with this stats question. I thought the answer was 1/3 by Bayes' Theorem, but I guess not? Here's the problem:

Sandhiya buys two new shirts for Diwali. The shirts on the rack are identical except for a sticker inside giving the name of the QA inspector and the day the shirt was inspected. Sandhiya picks two shirts at random from the rack. The sticker on at least one of the shirts says it was inspected by a woman, on a Saturday. If you assume the QA inspectors have an even chance to be men and women, and can inspect on any day of the week, then what is the probability Sandhiya chose two shirts that were both inspected by women?

Explanation / Answer

Suppose sandhiya choose first shirt which was inspected by women on Saturday and probablity=(1/7)*(1/2)

The Probability that second shirt inspected by women =1/2

So the Probability that Sandhiya choose first shirt which was inspected by women on Saturday and second shirt which was inspected by women =(1/7)*(1/2)*(1/2)=1/28

In the same way the Probability that first shirt which was inspected by women and second shirt which was inspected by women on Saturday =1/28

The Probability that two shirt inspected by women on Saturday =(1/7)*(1/2)*(1/7)*(1/2)=1/196

So the Probability that sandhiya choose two shirt which was inspected by women =(1/28)+(1/28)+(1/196)=15/196

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