A math question

[apomb]

is this still being debated? who won the bits?

[Insectoid]

r691175002 did. Still, feel free to debate it.

[apomb]

Meh, I can understand exactly how and why most people would think the way i originally assumed the question worked, however when i saw the solution and the other ways of stating the question, I just conceded that this is just another one of those debates that will divide message boards and break friendships. Just like the plane on a conveyer debate... its not even a debate, just different ways of stating a question as to make one group of thinkers believe they have fooled the other group.

tl;dr : Pointless internet debates are pointless

[Insectoid]

Hmm, Good answer, maybe it should be added to the poll (not really).

I agree with you, the only reason I posted this was to prove to my mom that she was wrong. And now that that has been accomplished, I suppose this thread can die happy.

[Reality Check]

Ah the Monty Hall Problem. This is why I love probability.

Here's another:

You have a neighbour with two kids.

Situation 1
You see outside the window and notice that one of the kids is a boy. What are the odds that the other is a girl?

Situation 2
You see outside and notice one of the kids is a boy. You strike up a conversation with him and find that he is the eldest child in the family. What are the odds that the other is a girl?

Tip: This is conditional probability

[Clayton]

1: 50%
2: 75%

[CodeMonkey2000]

Mabey I misinterpreted the question, but isn't the probability for both situations 50-50? How does being the eldest affect gender? Unless I missed something....

[Brightguy]

insectoid @ Tue Jun 03, 2008 7:54 am wrote:

So shut up and use the monty hall one, and foget it.

"If your solution doesn't fit the problem, change the problem", to paraphrase Einstein.

insectoid @ Wed Jun 04, 2008 9:17 am wrote:

I agree with you, the only reason I posted this was to prove to my mom that she was wrong. And now that that has been accomplished, I suppose this thread can die happy.

You added in the part about Monty afterwards! Your Mom was right.

[Reality Check]

They are in fact not the same. Think of all outcomes in a family of two kids. We have:

Two boys
older boy younder girl
younger boy older girl
two girls.

In other words: BB BG GB GG

We are told that one of them is a boy so that rules out the GG prossibility. We now have BB BG GB. So, the probability that the other is a girl for the first situation is in fact 2/3. For the second situation we do the same. GG was ruled out and now that we know the boy is older we can now rule out GB as well. We are now left with BB and BG. Therefore the probability in the second situation is in fact 1/2. Many will disagree I am going to assume...

[btiffin]

I apologized to insectoid privately for changing his cool math problem to a "heated" discussion. Was not my intent when I posted; being the old guy I was more trying to fill in the august members of compsci who the ever famous Monty Hall was and the reference to Let's Make a Deal.

If you read the wikipedia entry on Monty Hall Problem you will see how hard it is to word this problem to the satisfaction of a mathematician. No disrespect to insectoid was meant or deserved.

Great big

Cheers

[apomb]

btiffin, it must be the gentlemenly thing to do, i also appologised to insectoid privately for making it seem like this entire thing is pointless, i did not mean for it to be interpreted that way, i meant that the original question was answered, and people continued to argue against the blatantly correct answer.

[Tony]

Reality Check @ Wed Jun 04, 2008 10:29 pm wrote:

Many will disagree I am going to assume...

Yup. You've missed a couple of possible outcomes. Since you are distinguishing between older/younger sibling, then the order of boy/boy also matters. And so we get a sample space of:

B1B2 B2B1 BG GB G1G2 G2G1

Situation 1: one of the kids is a boy. Girl: 2/4 = 50% (B1B2 B2B1 BG GB)

[Reality Check]

I've never seen this argued the way you did Tony and it does make sense to me but I had 3 different teachers confirm that it was 2/3. One of which had a PHD in physics...

[A.J]

shouldn't we include the possibility that there could be twins (in case 1, where we see one of them being a boy)?

I might be just saying something stupid, so ignore me if I'm wrong.

[Tony]

Reality Check @ Wed Jun 04, 2008 11:18 pm wrote:

One of which had a PHD in physics...

Physics is not Statistics.

Maybe there's another explanation that leads to that answer, but as it stands -- the age of the child either matters for the sample space, or it does not. It seems inconsistent to say that the observed boy could have an older sister, a younger sister, or a brother of either age.