# Thread: Simple puzzles to stump people

1. Originally Posted by The_Liquid_Laser
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?
Yes. It is clear. But sometimes people play mental tricks on themselves.

I did that sort of thing on one of my finals last quarter and got the second lowest grade in the class (emabarasing )

2. The only one I've gotten so far was the letters/numbers card problem. The probability stuff is over my head. I usually sort of get it when it is explained, but I still don't understand why, for example, the sperm & egg of the second child would care what the gender of the first child was. It still seems like it should be 50/50 to me, although I can follow the reasoning in the solution.

3. Originally Posted by The_Liquid_Laser
My neighbor has two children. One of them is a boy. What is the probability that the other child is a girl?
I didn't look at the other responses. Is it this?

There are four potential combinations of two children:
BB
BG
GB
GG

Three combinations include at least one Boy.
There is a 2/3 chance for a combination of a boy and a girl.

4. Originally Posted by Ivy
The only one I've gotten so far was the letters/numbers card problem. The probability stuff is over my head. I usually sort of get it when it is explained, but I still don't understand why, for example, the sperm & egg of the second child would care what the gender of the first child was. It still seems like it should be 50/50 to me, although I can follow the reasoning in the solution.
The trip up for this one is that it doesn't say whether the boy (or girl if the question is asked that way.) is the first or second child. It gets read as "If the first child is a boy, the second child has a ...chance to be a girl", but is really, if either the first or second child is a boy, the other child has a ... chance of being a girl."

5. Originally Posted by Zergling
The trip up for this one is that it doesn't say whether the boy (or girl if the question is asked that way.) is the first or second child. It gets read as "If the first child is a boy, the second child has a ...chance to be a girl", but is really, if either the first or second child is a boy, the other child has a ... chance of being a girl."
OHHH, so it's not really a question of what are the chances of a child being born B or G, but what are the chances of a family with two children having a certain makeup? That makes so much more sense to me than how I had been seeing it before.

6. Originally Posted by Ivy
The only one I've gotten so far was the letters/numbers card problem. The probability stuff is over my head. I usually sort of get it when it is explained, but I still don't understand why, for example, the sperm & egg of the second child would care what the gender of the first child was. It still seems like it should be 50/50 to me, although I can follow the reasoning in the solution.
It took me a second to parse the question... The way I ended up rephrasing the question...

Given that one of the two kids will be a boy, what is the chance that there will also be a girl? The solution lists all the possible situation, eliminate the one that doesn't apply... and the solution comes from that. That's the mental gymnastics I did, anyway - it took me a bit to figure out what was being asked. For some reason I kept reading it as "The first child is a boy, what are the chances the second child is a girl" which isn't the same thing.

On one side I had a "previous flips do not matter" rule pounding in my head and I had to beat it into submission before I could even read the problem properly. Funny enough I probably would of been able to do it with a different context easier... I have children = "previous flips do not matter!" etched in my brain.

7. Yes Jennifer that is correct, and I actually appreciate the non-mathese explanations, like the one you gave, whenever they are possible.

8. Okay, then let's look at a slightly different problem along the same lines:

"My neighbor has two children. What is the probability that one of them is a girl?"

How would you parse this, then?

9. Originally Posted by oberon
Okay, then let's look at a slightly different problem along the same lines:

"My neighbor has two children. What is the probability that one of them is a girl?"

How would you parse this, then?

How many combinations of children are possible; how many fit the condition of containing a girl. (4 and 3, I believe).

10. Originally Posted by oberon
Okay, then let's look at a slightly different problem along the same lines:

"My neighbor has two children. What is the probability that one of them is a girl?"

How would you parse this, then?
It depends if you mean "at least one is a girl" or "exactly one is a girl". In a math context a person would generally assume that you mean "at least one is a girl".

If a person has 2 children then there are four possibilities: BB, BG, GB, GG.

So the answer is either 3/4 or 2/4=1/2 depending on what you mean.

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