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Yeah, this is a famous puzzle. The answer is supposed to be 2/3, because what the question is asking you to do is consider all the parents in the world where at

Yeah, this is a famous puzzle. The answer is supposed to be 2/3, because what the question is asking you to do is consider all the parents in the world where at least one of the two children is a girl. Then you're left with 3 possibilities, BG, GB and GG. If you phrase the question like that, everyone will get the right answer. The reason people get it wrong is that people don't normally talk like that. Imagine you're at a party, and someone tells you they have two kids, and "one of them is a girl." Clearly, they mean that the other is a boy, which means the answer is 100%. But the most intuitive way of interpreting the question is that you know that a specific child is a girl, say because the person brought one kid to the party, who turns out to be a girl. With this interpretation, the obvious answer of 50% is in fact correct. You often hear the complaint that people don't understand math. In this instance, however, an equally valid way of explaining what's going on is that mathematicians don't understand people. This criticism applies partially to the normal game-show version of the Monty Hall problem, but I think there the wording is genuinely ambiguous regarding the host's behavior, and my answer would be "not enough information."

biohacker42 18y ago
That's a good point and there a lot of people who are very good at math, but hate word problems with a passion.
hhm 18y ago
The game-show version of the Monty Hall problem isn't ambiguous... people even had the chance to see the show before knowing the mathematical problem. I agree there are different ways to state the problem, but the wording doesn't explain why it confuses people.
- procrastitron 18y ago
  Actually, the strongest criticism that I've heard about the Monty Hall problem is that the game show didn't actually work like that. I've tried explaining the problem to both people who've seen the show and those who haven't. My experience is that if you've seen the show you'll never accept the question, let alone the answer. Meanwhile, those who never watched the show can be convinced.
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soldarnal 18y ago
The BG vs GB thing is difficult to understand. But easier to understand is that 50% of two child familes are mixed gender, while 50% are same gender. With 40 families having two children, 20 will have a boy and a girl, and 20 will have either two boys or two girls. Of the same gender familes, 50% (10) will be boy/boy and 50% (10) will be girl/girl. If you learn that a particular family has a daughter, then you know that family isn't one of the 10 families with two boys. This leaves 30 families, 20 of which (or 2/3) have one boy. Likewise, for some reason the Monty Hall problem is hard to understand in three door form. But if you change the problem to 100 doors, and explain that Monty's assistant closes 98 bad doors, it's easier (at least for me) to see that the original guess had a 1/100 chance of being right, while the other door is 99/100 likely to be the right one.
raganwald 18y ago
> You often hear the complaint that people don't understand math. In this instance, however, an equally valid way of explaining what's going on is that mathematicians don't understand people. This is by far the most insightful thing I have ever read about this problem. Furthermore, this being a site about startups, I would say that you will be more successful if you understanding people and math than if you just understand math.

biohacker42 18y ago

That's a good point and there a lot of people who are very good at math, but hate word problems with a passion.

hhm 18y ago

The game-show version of the Monty Hall problem isn't ambiguous... people even had the chance to see the show before knowing the mathematical problem. I agree there are different ways to state the problem, but the wording doesn't explain why it confuses people.

procrastitron 18y ago
Actually, the strongest criticism that I've heard about the Monty Hall problem is that the game show didn't actually work like that. I've tried explaining the problem to both people who've seen the show and those who haven't. My experience is that if you've seen the show you'll never accept the question, let alone the answer. Meanwhile, those who never watched the show can be convinced.

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soldarnal 18y ago

The BG vs GB thing is difficult to understand. But easier to understand is that 50% of two child familes are mixed gender, while 50% are same gender. With 40 families having two children, 20 will have a boy and a girl, and 20 will have either two boys or two girls. Of the same gender familes, 50% (10) will be boy/boy and 50% (10) will be girl/girl. If you learn that a particular family has a daughter, then you know that family isn't one of the 10 families with two boys. This leaves 30 families, 20 of which (or 2/3) have one boy. Likewise, for some reason the Monty Hall problem is hard to understand in three door form. But if you change the problem to 100 doors, and explain that Monty's assistant closes 98 bad doors, it's easier (at least for me) to see that the original guess had a 1/100 chance of being right, while the other door is 99/100 likely to be the right one.

raganwald 18y ago

> You often hear the complaint that people don't understand math. In this instance, however, an equally valid way of explaining what's going on is that mathematicians don't understand people. This is by far the most insightful thing I have ever read about this problem. Furthermore, this being a site about startups, I would say that you will be more successful if you understanding people and math than if you just understand math.