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More unintuitive probability


Jun 3 2010, 10:11 PM (Post #1)
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QUOTE
I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?


I believe it's 50%, but ofc I'm wrong. Damn probability.
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Jun 4 2010, 04:36 AM (Post #2)
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BG
GG
GB
BB

are the four possibilities, each equally likely. You've eliminated GG. BB is 1/3 of the remaining set.
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Jun 4 2010, 05:45 AM (Post #3)
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Since it's genetics, I think it would be 50%. I think, like a coin flip, it's always 50%.
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Jun 4 2010, 03:07 PM (Post #4)
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The answer my professor gave was different from both of yours.

# of ways first child is a girl born any day of week, second is boy on tuesday: 7
# of ways first child is a boy born on tuesday, second is a girl born any day of week: 7
# of ways first child is a boy not born on tuesday, second child is a boy born on tuesday: 6
# of ways first child is a boy born on tuesday, second child is a boy not born on tuesday: 6
# of ways first child is a boy born on tuesday and second child is a boy born on tuesday: 1

total possibilities: 7 + 7 + 6 + 6 + 1 = 27
how many of them involve two boys? 6 + 6 + 1 = 13

So the probability is 13/27 (~48%)
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Jun 4 2010, 11:02 PM (Post #5)
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This might even be a case of NEI. (Are they born in the same week? How would that be possible? What is the meaning of 'Tuesday'?)
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Jun 6 2010, 01:31 AM (Post #6)
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QUOTE (Jinghao @ Jun 3 2010, 11:36 PM)
BG
GG
GB
BB

are the four possibilities, each equally likely. You've eliminated GG. BB is 1/3 of the remaining set.
*



true words.

QUOTE
This might even be a case of NEI. (Are they born in the same week? How would that be possible? What is the meaning of 'Tuesday'?)


Tuesday is too much information; it's largely irrelevant.
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Jun 10 2010, 04:08 PM (Post #7)
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I don't really buy the whole Tuesday being relevant bit.

I did want to make a dice game though based on the probability of rolling two 1's (or some other number) given that you've rolled at least one.
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Jun 11 2010, 01:12 AM (Post #8)
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Is there more to this problem or what? Do you have two kids at the same time? ....what is the point of this question?
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Jun 11 2010, 03:10 AM (Post #9)
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To show that if you have a son born on tuesday, you're more likely to have a daughter than a second son.
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Jun 11 2010, 06:13 AM (Post #10)
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QUOTE (AWESOM-O @ Jun 10 2010, 10:10 PM)
To show that if you have a son born on tuesday, you're more likely to have a daughter than a second son.
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And, by that logic, it follows that the elimination of pirates in the Atlantic also contributed to global warming.
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Jun 12 2010, 12:28 AM (Post #11)
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Wait a second, isn't this the gambler's fallacy?
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Jun 12 2010, 12:37 AM (Post #12)
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iirc, no. A person sees one event pop up a lot, so they think a different event is more likely to pop up next time. ie flip 100 heads, so the next one must be tails to equalise the 50-50 odds. (Reverse gambler's fallacy saying 100 heads appeared, so the next one must be heads too)
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Jun 12 2010, 12:45 AM (Post #13)
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QUOTE (AWESOM-O @ Jun 11 2010, 07:37 PM)
iirc, no. A person sees one event pop up a lot, so they think a different event is more likely to pop up next time. ie flip 100 heads, so the next one must be tails to equalise the 50-50 odds. (Reverse gambler's fallacy saying 100 heads appeared, so the next one must be heads too)
*



In a sequence of two coin flips, you have these possible options

HH
HT
TH
TT

Since TT is eliminated, you have a 66% chance of getting HT (TH). Isn't that the same thing?
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Jun 12 2010, 01:32 AM (Post #14)
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QUOTE (Simply Fabulous @ Jun 11 2010, 07:45 PM)
In a sequence of two coin flips, you have these possible options

HH
HT
TH
TT

Since TT is eliminated, you have a 66% chance of getting HT (TH). Isn't that the same thing?
*


No. They recognise the two events are unaffected, and they know what the sample space is, unlike your example. The Gambler's fallacy says "I know what probability says, but I think the universe works in a certain way when it comes to the law of large numbers. Either it will equalize (GF) or the universe is biased towards x (RGF)"
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Jun 12 2010, 02:09 AM (Post #15)
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QUOTE (AWESOM-O @ Jun 11 2010, 08:32 PM)
No. They recognise the two events are unaffected, and they know what the sample space is, unlike your example. The Gambler's fallacy says "I know what probability says, but I think the universe works in a certain way when it comes to the law of large numbers. Either it will equalize (GF) or the universe is biased towards x (RGF)"
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I get all that. I misread the question, under the assumption that the second child hadn't been born yet, and in an amazing display of ineptitude, I threw myself off.

This post has been edited by Simply Fabulous: Jun 12 2010, 02:11 AM
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