What is the answer to tonight's math conundrum?

[alarcojon]

The following question was asked in this thread:

http://www.democraticunderground.com/discuss/duboard.php?az=view_all&address=105x4172827

You are going to your friends house. You know your friend has two children. When you arrive at the house and knock on the door a young boy answers the door. What are the odds that the other child is a boy as well?

What do YOU think the answer is?

[aePrime]

1. See this post

http://www.democraticunderground.com/discuss/duboard.php?az=show_mesg&forum=105&topic_id=4172827&mesg_id=4173711

It's proven with conditional probability. I've even cited sources.

[alarcojon]

3. See my post 67 in the same thread

and tell me what is wrong with it.

[billyskank]

10. Can't fault it

Although it does fuck with your head. Probability is like that.

[hfojvt]

2. what about this one

three guys stay at a hotel, pay $10 each. The hotel owner decides he charged too much and gives the bell boy $5 to give back to them. The bell boy pockets $2 and gives them each a dollar back. Thus they each paid $9 for their room. 9 x 3 is 27. 27 plus 2 is $29, what happened to the other dollar?

[jpgray]

4. It's impossible to answer as asked

Mathematically, if you "flip" twice, you are twice as likely to get one boy and one girl in some order than two boys in a row. Yet at the same time, as a pair two boys are 100% likely to provide your knock with a boy answer, whereas a boy/girl pair can only be less likely. My contention is that there's no way to determine how much less likely because there is no neat mathematical formula for human behavior. I assumed that the boy always answers and that there is no chance for the girl to answer. That's not real life, but taking this to real life would make this question unanswerable.

If you treat it with coins to avoid the confusing-as-hell human element, and say your friend flipped two under a box and revealed one at random as heads, and then asked you the odds the other was heads, it would be 50%. Because while your friend remains twice as likely to get one heads and one tails in some order than he is to get two heads in a row, two heads would have twice the chance of revealing one heads when one coin is shown at random, as compared to a pair consisting of one heads and one tails.

I saw the question more as: your friend flips a coin twice, and tells you once it was heads--what are the odds that the other time it was heads? In this case the answer is 1/3.

[Az]

5. Just to reiterate... I did say there would be wailing and gnashing

:evilgrin:

[alarcojon]

6. Not, however, on my end

B-)

[jpgray]

7. I'll never accuse you of getting tied up with something again

:scared:

:D

[alarcojon]

8. You DO know how I voted in that other poll...

...oh revered one.

[jpgray]

9. You're fairly venerable yourself

But I can't vote in this poll. I have to say the question is unanswerable as given, though it would be some amount more than 1/3 if either gender can and will answer the door. I must confess I never considered the possibility that the girl could answer, and assumed it was along the lines of those old Carroll logic problems with monochromatic knights and knaves--archetypes that are totally divorced from reality. In the world I assumed for this problem, I suppose, only boys can answer doors.

:crazy: