Thread: looking for clarification on a simple argument

So I'm sure anyone who likes probability and statistics enough has heard of this type of question. It goes something along the lines of:

A mother takes her son, out of two kids, to the park. What is the probability her other child is a girl?

And I would say 2/3. Because the 4 possible ways of having 2 kids are BB GG BG and GB. So the option GG is eliminated, and of the remaining 3 options another boy occurs once, a girl occurs twice.

Now on the flip side... if the question said:

A mother takes her oldest son, out of two kids, to the park. What is the probability her other child is a girl?

Again... the four possibilities are BB, BG GB and GG. Is birth order relevant to this question? Would the answer still be 2/3 or would it be 1/2 because the option BG is eliminated from the set (assuming girl is the older child in the option BG)

Originally Posted by sonictech

So I'm sure anyone who likes probability and statistics enough has heard of this type of question. It goes something along the lines of:

A mother takes her son, out of two kids, to the park. What is the probability her other child is a girl?

And I would say 2/3. Because the 4 possible ways of having 2 kids are BB GG BG and GB. So the option GG is eliminated, and of the remaining 3 options another boy occurs once, a girl occurs twice.

Now on the flip side... if the question said:

A mother takes her oldest son, out of two kids, to the park. What is the probability her other child is a girl?

Again... the four possibilities are BB, BG GB and GG. Is birth order relevant to this question? Would the answer still be 2/3 or would it be 1/2 because the option BG is eliminated from the set (assuming girl is the older child in the option BG)

If you're asking a question, then here's the answer:

The unrestricted sample space is BB, BG, GB, GG where the younger child is first and the older child second. But what you're calculating is a conditional probability viz. Pr(younger child is G | Older child is B).

Then the restricted sample space is BB, GB.

So the answer is clearly 1/2.


For the first part, you're correct:

You're calculating a conditional probability viz. Pr(One child is G | One child is B).

Then the restricted sample space is BB, GB, BG.

So the answer is clearly 2/3.

good, so we're in agreement. Maybe now my friends will get off my back :P

thanks!