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**More unintuitive probability**

I Love Jingy |
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Not Odd anymore |
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I Love Jingy |
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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

# of ways first child is a boy born on tuesday, second child is a boy

# 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%)

# 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%)

General |
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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.

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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I Love Jingy |
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I Love Jingy |
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General |
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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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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?

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)"

General |
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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)"

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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