06-02-2002 04:56									#1
	A woman has two children, at least one of which is a boy... Support Apolyton, buy Call to Power 2

The probability that the other child also is a boy is thus 1/3.

Is this correct or incorrect?

	06-02-2002 04:59									#2
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incorrect.

	06-02-2002 04:59									#3
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*runs from Maths Stats*

	06-02-2002 05:06									#4
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There are 4 equally likely situations, given no info. These are

Bb, Bg, Gb, Gg - where the size of letter indicates oder of birth.

Gg is ruled out by the statement that she has at least one boy. In only 1 case of the 3 remaining does she have 2 boys, so the probability is 1/3

Note - this changes if you specify some defining feature about the stated boy that only one of a pair could possess - such as being the eldest. Then the probability, as expected, becomes 1/2

	06-02-2002 05:06									#5
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Loinburger..please explain.

	06-02-2002 05:08									#6
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With two children there are four equally probable outcomes:
1. Both are boys;
2. First is a boy, second is a girl;
3. First is a girl, second is a boy;
4. Both are girls.

By definition, outcome #4 is excluded, so we have three left. Only one of these has a boy as the other child. Therefore the probability is indeed 1/3.

Edit: Chowlett said the same thing, but got his post in ahead of me.

	06-02-2002 05:12									#7
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from what I understand, correct, but unfortunately I'm always told that my understanding of prob stat is off

	06-02-2002 05:30									#8
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Buggerall.

	06-02-2002 05:37									#9
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What about other alien species?

	06-02-2002 05:39									#10
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quote: Originally posted by Imran Siddiqui What about other alien species?

The argument holds assuming they have a 1:1 distribution of male and female births.

	06-02-2002 05:44									#11
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If we postulate a species which has three sexes, evenly distributed, one of which is male, then the probability is 1/5. Proof is left as an exercise to the student. . .

	06-02-2002 05:48									#12
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It's got to be 50% the way I see it, but I'm probably just a stoopid hippy...

	06-02-2002 05:51									#13
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It's 1/2. The probability of either offspring being a boy is 1/2. If you know what one is, then the problem reduces to: a woman has one child of unknown gender: the probability it's a boy is: ___

The two births are independent events.

	06-02-2002 05:51									#14
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quote: Originally posted by Chowlett The argument holds assuming they have a 1:1 distribution of male and female births.

But assuming only makes an ass out of you and me .

	06-02-2002 05:53									#15
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On the other hand if you are looking at the population of women with 2 children at least one of which is a male, then yes, the probability of the other being a male is 1/3... so it really depends on how the problem is worded and what it's asking for.

	06-02-2002 05:54									#16
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Victor beat me to it. Some of our Apolyton posters obviously didn't pay attention in High School.

	06-02-2002 05:57									#17
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Ah, that means I'm actually a genius hippy! Now if I could only figure out how to implement the dope smokin' smiley...

	06-02-2002 06:00									#19
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oops

	06-02-2002 06:02									#20
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These problems always piss me off. Like the one, "You are on a game show where you must choose Door Number 1, 2, or 3; there is a prize behind one of the doors, and nothing behind the other two. You choose Door 1. The host then reveals that there was nothing behind Door 3, and asks if you would like to change your answer to Door 2. Do your odds of winning increase, decrease, or stay the same if you now change your response from Door 1 to Door 2?

	06-02-2002 06:08									#21
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quote: Originally posted by loinburger These problems always piss me off. Like the one, "You are on a game show where you must choose Door Number 1, 2, or 3; there is a prize behind one of the doors, and nothing behind the other two. You choose Door 1. The host then reveals that there was nothing behind Door 3, and asks if you would like to change your answer to Door 2. Do your odds of winning increase, decrease, or stay the same if you now change your response from Door 1 to Door 2?

Increase.

	06-02-2002 06:10									#22
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quote: Originally posted by loinburger These problems always piss me off. Like the one, "You are on a game show where you must choose Door Number 1, 2, or 3; there is a prize behind one of the doors, and nothing behind the other two. You choose Door 1. The host then reveals that there was nothing behind Door 3, and asks if you would like to change your answer to Door 2. Do your odds of winning increase, decrease, or stay the same if you now change your response from Door 1 to Door 2?

Your chance of winning increases to 1/2 from 1/3, but it makes no difference which door you pick - you have fifty/fifty odds. So in short, stay the same.

	06-02-2002 06:13									#23
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We batted the three-door problem around on another thread quite awhile back. That one definitely depends on how the problem is stated. If the host says "I'm going to open door #3, I don't know what's behind it" and it turns out to be empty (and he was telling the truth), then your odds don't change if you switch. But if he says "Of the doors you didn't pick, I'm going to open one that has no prize" your odds go up from 1/3 to 2/3 if you switch.

Last edited by Rex Little on 06-02-2002 at 06:26

	06-02-2002 06:30									#24
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quote: Originally posted by Rex Little We batted the three-door problem around on another thread quite awhile back. That one definitely depends on how the problem is stated. If the host says "I'm going to open door #3, I don't know what's behind it" and it turns out to be empty (and he was telling the truth), then your odds don't change if you switch. But if he says "Of the doors you didn't pick, I'm going to open one that has no prize" your odds go up from 1/3 to 2/3 if you switch.

Precisely. Basically, since door three is open, swapping is like choosing both doors 2 and 3.

Or another way - choose door 1. Either you're wrong (probability 2/3) or right (1/3). Therefore once door three is ruled out, changing to 2 will make you right is you were wrong (2/3) and wrong if you were right (1/3). so plainly, it's better to swap.

	06-02-2002 07:37									#25
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I believe females make up 52% of the population. Therefore there is a 48% chance of the next child being a male.

	06-02-2002 08:10									#26
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Actually, ~52% of all born children are male. But infant mortality is higher among males, thus equalizing the scale... as far as I know, these phenomens are yet unexplained. But then, it has pretty much nothing to do with this little brainstorming session.

	06-02-2002 08:12									#27
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Nonsense. Once door #3 is revealed both door 1 and 2 offer the same odds. (1/2)

	06-02-2002 08:12									#28
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not to threadjack but...

I thought for sure it was 52% female. This was to account for the fact that women are more likely to be infertile and unable to reproduce than men due to their biology.

	06-02-2002 09:12									#29
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The basic assumption you're making in this problem (if the answer is 1/3) is that there's no relevant distinction between the two boys (since it makes no difference which boy comes first, there's only one boy-boy combo in the set of possibilities, whereas there are two boy-girl combos - one in which the boy comes first and the other, the girl comes first).

	06-02-2002 09:18									#30
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D'oh, already written by Chow.