# Thread: Probability question making my brain hurt :p

1. ## Probability question making my brain hurt :p

"suppose you know that a friend of yours has two children and that at least one of them is a boy. One day, you visit your friend's house and his son opens the door when you knock. What is the probability that he has two sons?"

I kind of felt like it would be higher than 50% seeing as he already knew there was a son. Thoughts?

Thankyou ^.^

2. ## Re: Probability question making my brain hurt :p

The question says that you know your friend has two children, at least one of which is a boy. Thus, the possible combinations of your friend’s children are B+B, B+G and G+B. Assuming that boys and girls are equally likely, each of these three possibilities has the same probability. However, only one of them is the desired B+B, and so the probability is 1/3, assuming further that it is equally likely that either of your friend’s two children will open the door.

Note also that we count B+G separate from G+B because they are different possibilities of mixed genders.

The problem would be different if you knew only that your friend has two children but nothing about any of their genders. In that case, the answer would be 1/2. Variants of this problem have a long history.

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