Disney Magic

I was at Disneyland and decided to conduct a survey of the families. I asked people at random if they have exactly two children. And if so, if one of them was a boy born in January.

After a while, I finally found someone who said yes. What is the probability that this person has two boys?

Assume that there is an equal chance of either sex, and equal chance of being born in any month of the year.

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