Bizarre Probability Problem (1 Viewer)

FullMonte

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I was watching a video today explaining a bizarre problem involving probabilities. It has two parts.

Part 1
You meet a man in a bar who tells you that he has two children. He tells you that one of his children is a girl (now, she does have a name, but he doesn't mention it).
What is the probability that his other child is also a girl? (Hint: It's not 1/2)


Part 2
You meet a man in a bar who tells you that he has two children. He tells you that one of the children is a girl, and her name is Debra.
What is the probability that his other child is also a girl? (Hint: it's not the same answer as the part one)
 

lapaz

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How did I not catch the first one? Nice work. :9:
He told us it was a trick question, so I thought I better read very carefully. The wording was almost identical, but just a couple of words changed, so I honed in on those. It was a fun little mind exercise of parsing words.
 

superchuck500

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The probability that the other child is a girl is 0 for Part 1, because he said he only has 1 girl. Part 2 is 50%.
Seems to me as well - but that's where it gets semantic. In part 1 he says "one of my children is a girl", and yes it strongly suggests that it means that he's identifying which portion of the whole is female (leaving the remainder to be not female). But literally, that's not the only meaning. He could just be a smart-arse that plays word games - my dad does that crap with me all the time

So your other child must be a boy? No, I didn't say that. I just said one of them is a girl. The other one is too, but was I wrong?
 
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FullMonte

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The probability that the other child is a girl is 0 for Part 1, because he said he only has 1 girl. Part 2 is 50%.
No, he didn't. He didn't say that he only had one girl. He said that he had two children, and that one of them is a girl. There are two possibilities for the other child. The other child could be a girl, or the other child could be a boy. However, having only two possibilities does not translate into a 50% probability.

I'll explain Part 1. The correct answer is 1/3, or 33%. With two children, there are four possible combinations
Boy/Boy
Boy/Girl
Girl/Boy
Girl/Girl

Since he said that one of his children is a girl, that means there are three possible combinations (B/G, G/B, G/G). Of those three, in only one case is the other a girl.



He told us it was a trick question, so I thought I better read very carefully. The wording was almost identical, but just a couple of words changed, so I honed in on those. It was a fun little mind exercise of parsing words.
I didn't say it was a trick question. I said it was a bizarre probability problem. The bizarre part is not in any kind of trickery in the wording. The bizarre part is that telling us the name of his daughter actually changes the probability that the other child is also female.
 

DaveXA

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Yeah, I thought it might be 33%. 25% would have been correct if we didn't know the sex of either of them. But, the way it's worded, it could be 0% it looks lile to me.
 

lapaz

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Seems to me as well - but that's where it gets semantic. In part 1 he says "one of my children is a girl", and yes it strongly suggests that it means that he's identifying which portion of the whole is female (leaving the remainder to be not female). But literally, that's not the only meaning. He could just be a smart-arse that plays word games - my dad does that crap with me all the time

So your other child must be a boy? No, I didn't say that. I just said one of them is a girl. The other one is too, but was I wrong?
That's a lawyerly perspective. However, mathematically he would be wrong if he said that one of his children is a girl, if he actually has two girls, because mathematically he has two girls. Since this is a math problem, mathematical language trumps semantics. Besides it would make the question wrong, since it would result in both probabilities being equal to 50%, so the obvious intent was to identify the portion of the whole.
 

superchuck500

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That's a lawyerly perspective. However, mathematically he would be wrong if he said that one of his children is a girl, if he actually has two girls, because mathematically he has two girls. Since this is a math problem, mathematical language trumps semantics. Besides it would make the question wrong, since it would result in both probabilities being equal to 50%, so the obvious intent was to identify the portion of the whole

115171
 

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