You meet a man who tells you he has two children. One of his kids walks into the room and it is a boy. What is the probability the other kid is also a boy.

Question

anonymous · Answer

1/2. Either he's a boy or a girl, so it's a 50/50 chance.

anonymous · Answer

50%, the gender of one child does not affect the gender of the next.

anonymous · Answer

both of you are wrong!

anonymous · Answer

How so?

anonymous · Answer

let me rephrase the question: if you know someone has 2 children, at least one of which is a boy, what is the probability he has 2 boys?

anonymous · Answer

1/3

anonymous · Answer

blam!

anonymous · Answer

Combinatorics baby.

anonymous · Answer

25 % boy 75% girl

anonymous · Answer

not quite.

anonymous · Answer

He has two children do you  started of with two 50/50 chances or 4 chances at 25%

anonymous · Answer

Sets: {A=boy ,B=boy} {A=girl ,B =boy}{ A=boy, B=girl}, {A =girl, B=girl}
Given a child is a boy, we can remove the double girl set, leaving three sets. A=boy, B=boy is thus 1/3.

anonymous · Answer

OK 4 variations on boy girl we know girl girl can not happen so only  1 of the last 3 can happen so 1/3

anonymous · Answer

It's counter-intuitive math, but perfectly logical if you work through it, which is why I like it so much.

anonymous · Answer

it's one of my favorite probability / combinatorics questions because it's so counter-intuitive. If someone has no background in math, you can get in an hour long discussion about why it's not 50%.