Math Is Fun Forum

Nuh uh! I got that point fair and square.

Well, I still think your leap of logic is bigger than mine.
But anyway, both versions of the question have been answered, so the poster should be happy.

He calls them line segments. For me, that makes things fairly unambiguous.

Yes, those are the only possiblities. But they're not equally likely.
You can try it yourself, by flipping coins. Flip 2 coins at a time and the possible results are:

- Two heads
- Two tails
- One of each

The third result should come up roughly twice as much as the other two.

It's an interesting question though, MIF. I've half got my head around it now.

The two extremes of the question are:
"I have two children. This one here, who I'm directly pointing at with no possiblility for confusion, is a boy. What's the probability that I have two boys?"
Answer 1/2.

"I have two children. One of them, and I'm not giving you any information about which, is a boy.
What's the probability that I have two boys?"
Answer 1/3.

The rest of this type of question form a 'sliding scale'. The probability depends on how likely it is that the given information could describe either child.

So, if he says "One of them likes ice-cream and is a boy", then the answer is close to 1/3, since clearly everyone loves ice-cream.

With the Tuesday clue it's less likely that the two children could be confused, and so the answer is closer to 1/2.

If you said that one child was born on Tuesday while football was on TV and it was a bit cloudy and in the room next door somebody was listening to Lady Gaga, and is a boy, then you're almost certainly specifying the child you mean. So the probability there is 1/2 - ε

Cracked it. Hopefully.

Interestingly, you can take a shortcut with this puzzle by "meta-thinking", making the assumption that there is a single correct answer.

"I was telling my friend about a survey I took about house numbers. I told her how many houses were surveyed, and the sum of the surveyed house numbers. She knew that my number was even, and then she managed to figure out what my number was.

What's my house number?"

Nice page!

Two things:
- When you click on the cell of a matrix, I think it'd be good if the current contents got highlighted so you can type over them.

- When a result has a big negative number (big in size, so -0.00001 would count) then trying to transcribe the result over to a matrix makes that cell only display "-". The value is stored properly though, so it's just a visual thing.

This thing is scary.

It asked me 19 questions, and I gave it maybe 4 yesses and 15 nos. It didn't seem to be focussing in on anything in particular. As far as I can tell, the only thing it knew about my character is that he is a British adult male who works on TV.

Then out of nowhere, the right answer comes up.
I really have no idea how that could have happened.

I can't find that problem on the page you linked, but I agree with your answer. Given that no bus has come in 20 minutes, the waiting time has to be somewhere in the interval [0,40].