# Thread: Probability question (boys & girls)

1. ## Probability question (boys & girls)

Hi, I'm new to this site. Sorry I'm jumping in with a question as the first post!

There was a question in my textbook that goes like this:
"A family has 2 kids. Given that at least one of them is a boy, what is the probability that both of them are boys?"

Initially the kids could satisfy one of three cases:
boy/boy, boy/girl, girl/girl
But now that we are given that at least one of them is a boy, we can eliminate the case girl/girl. Out of the two remaining cases, one is favorable, so the probability should be 1/2.

But the answer as given in the book is 1/3. What am I doing wrong?

2. Originally Posted by whitehat
Hi, I'm new to this site. Sorry I'm jumping in with a question as the first post!

There was a question in my textbook that goes like this:
"A family has 2 kids. Given that at least one of them is a boy, what is the probability that both of them are boys?"

Initially the kids could satisfy one of three cases:
boy/boy, boy/girl, girl/girl Mr F says: You've missed an 'outcome': girl/boy. See below.

But now that we are given that at least one of them is a boy, we can eliminate the case girl/girl. Out of the two remaining cases, one is favorable, so the probability should be 1/2.

But the answer as given in the book is 1/3. What am I doing wrong?

You're given that at least one is a boy. So the reduced sample space is:

BG
GB
BB

where the younger sibling is given first.

So the probability that both are boys is 1/3.

3. ## Thanks

Oh... I didn't consider them as two separate entities. Thanks!