[OT] mathematical query

[Xeriar]

Now I know what my math teacher meant when he said: "probability problems are too hard to correct, that's why there is none for the exam to get into engineer school"

Believe me, they are on the exam to become one...

 

[2WS-Steve]

Did you see my posts on these two problems? They both come down to the assumptions. Both answers to both problems can be defended, given appropriate assumptions.

Sorry CR. You gave the solution to the 2 kids problem earlier in the thread but it seemed like people weren't understanding your answer.

However, I don't think there are many reasonable assumptions one can make that issues in the correct chance of the other kid being male being something other than 50%.


The Monty Hall case *does* depend on the assumption you point out in your more recent post regarding it. Most people reading the problem probably take it in the "Let's Make a Deal" way and I'm pretty certain that's the way Monty Hall actually played the game.

 

[2WS-Steve]

Now I know what my math teacher meant when he said: "probability problems are too hard to correct, that's why there is none for the exam to get into engineer school"

They are awfully hard to get right; as CRGreathouse pointed out, assumptions sneak their way in all the time. That said, I've found that using Bayes' Theorem helps make explicit any unstated assumptions and gets you the right answer. When there is disagreement you can more easily isolate which variable is causing the problem.

 

[CRGreathouse]

Sorry CR. You gave the solution to the 2 kids problem earlier in the thread but it seemed like people weren't understanding your answer.

That's just fine - I wanted to make sure you knew what I said (either to agree, or to prove me wrong).

However, I don't think there are many reasonable assumptions one can make that issues in the correct chance of the other kid being male being something other than 50%.

That's my 'marble' analogy. If you asked someone with 2 kids if they had a son and they said yes, there's a 2/3 chance their kids have different genders, as far as I can tell:

MM
MF
FM
*FF*

If you ask them the gender of their first child and they say "male", the chance becomes 1/2:
MM
MF
*FM*
*FF*

Agreed?

 

[Blacksad]

Believe me, they are on the exam to become one...

There wasn't any on mine (e3a, CCP, CS)

Perhaps, what my teatcher said was "no more" because they have experimented with that.

 

[2WS-Steve]

That's my 'marble' analogy. If you asked someone with 2 kids if they had a son and they said yes, there's a 2/3 chance their kids have different genders, as far as I can tell:

MM
MF
FM
*FF*

Yah, that's right; there's a 75% chance they'd answer yes in the first place; if they do so then 2 out of the three times they'd have different gendered kids.

If they answered "no" there'd be a 0% chance they had different gendered kids. That covers all the possibilities.

I think the way you phrased the problem is the way it's usually put and perhaps the way Sigil interpreted the original question.

 

[CRGreathouse]

Yah, that's right; there's a 75% chance they'd answer yes in the first place; if they do so then 2 out of the three times they'd have different gendered kids.

If they answered "no" there'd be a 0% chance they had different gendered kids. That covers all the possibilities.

I think the way you phrased the problem is the way it's usually put and perhaps the way Sigil interpreted the original question.

I completely agree.

I also thought that the original question is more like the other situation I described, making the chance 50/50, as we both concluded.

 

[LightPhoenix]

The king either chose the right potion or he chose the wrong one. Therefore the probability is 100% or 0%.

By the way, blatantly tounge-in-cheek.

LightPhoenix

 

[2WS-Steve]

The king either chose the right potion or he chose the wrong one. Therefore the probability is 100% or 0%.

By the way, blatantly tounge-in-cheek.

LightPhoenix

Actually there are some professional philosophers who defend exactly that position.

 

[MeepoTheMighty]

Ugh. And they wonder why I got a D in Stat Mech.