# Thread: Simple puzzles to stump people

1. Originally Posted by The_Liquid_Laser
(The problem below assumes that when a woman gives birth there is an equal chance of the child being either a boy or a girl.)

My neighbor has two children. One of them is a boy. What is the probability that the other child is a girl?
Solution..
For combinations of 1st and 2nd child, we have
p(BB) = p(BG) = p(GB) = p(GG) = .25

those including boys have X = p(BB or BG or GB) = .75
and of those including girls Y = p(BG or GB) = .5,
and the probability is given by Y/X = 2/3.

2. Yes Santtu that is correct.

3. Originally Posted by athenian200
I really think only an IxTP could just accept logic like that without an inner struggle (that's their primary strength).
Well with doing few mathematical exercises, you could probably catch on fast. After a while, it's easy to recognize when some statement is given in the language of mathematics. Usually the whole situation is then completely described in the statement given and no outside influences are allowed, except for knowing how to calculate, of course.

It doesn't mean that mathematicians wouldn't care about the real life! It's just that it's impossible to transfer the whole world to the language of mathematics with all it's nuances. That's why the world is there, to be lived and experienced. Using mathematics, one is bound to consider only limited aspects of it an any one time, or the problem would be ill-defined. I believe that mathematicians are often extremely interested of the applied parts, i.e. where the theory meets the world. Sometimes some concepts are generated more for the mathematical community rather than for the public.

One analogy could be that of business-to-business sales and selling to consumers: both are needed.

In short, mathematics is for well-defined problems, but humans excel in ill-defined problems. There's also interesting mixes of the two such as recommendation systems, neural nets, pattern recognition etc.. the methods may be strict, but in the end, it's the human who judges how well a problem is really solved.

4. Originally Posted by The_Liquid_Laser
No the answer is not 1/2. I can assure you that the problem I'm presenting is not equivalent to the one you are describing with coin flips.
Even here, interpreting the problem statement is where a lot of the problem lies.

Some people may interpret the problem to mean that your neighbor is about to have a second child (a misinterpretation, but seems to be common), instead of already having two children.

I guess Santtu already posted the spoiler, but I have always been fascinated by how people make mistakes. It would have been interesting to see what other answers people came up with.

5. Originally Posted by ygolo
I guess Santtu already posted the spoiler,
Sorry, was the answer too visible? I tried to select a color that would blend into the background.

6. Originally Posted by Santtu
Sorry, was the answer too visible? I tried to select a color that would blend into the background.
I think it's fine. I personally find white harder to read, w/o highlighting.

7. Originally Posted by The_Liquid_Laser
No the answer is not 1/2. I can assure you that the problem I'm presenting is not equivalent to the one you are describing with coin flips.

8. Darn, I haven't gotten any of these right... I've only managed to make myself feel stupid. I must be the thickest person here. I just don't think this way, there's too many variables, and too many specific technicalities and rules that affect the answer that aren't immediately apparent. How do you manage to think like this? You'd have to be a rocket scientist.

9. Originally Posted by ygolo
Even here, interpreting the problem statement is where a lot of the problem lies.

Some people may interpret the problem to mean that your neighbor is about to have a second child (a misinterpretation, but seems to be common), instead of already having two children.

I guess Santtu already posted the spoiler, but I have always been fascinated by how people make mistakes. It would have been interesting to see what other answers people came up with.
This is what I said. "My neighbor has two children. One of them is a boy. What is the probability that the other child is a girl?"

I admit it's easy to misinterpret a problem the first time it is read, but I don't think the wording is unclear. Isn't it clear that the neighbor already has two children?

10. Originally Posted by athenian200
Darn, I haven't gotten any of these right... I've only managed to make myself feel stupid. I must be the thickest person here. I just don't think this way, there's too many variables, and too many specific technicalities and rules that affect the answer that aren't immediately apparent. How do you manage to think like this? You'd have to be a rocket scientist.
A lot of these problems have success rates of 1 in 10 or something, despite the initial appearance of being "simple".

I didn't get the Monty Hall problem the 1st time I saw it, either.

But the basic idea to understand is Conditional Probability.

Besides that the way to think about a probability problem is to imagine running a whole bunch of "experiments" of the problem statement in parallel, chosing the parameters according to known probability distributions.

I may post something more detailed after work (unless someone beats me to it) or if I have some down time. I've been really busy today.

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•