Lot's of variations of 2, sort of like that 2+2=2*2=2^2 issue along with poking you in the proverbial eyeball because you want from the start to say 50/50 because you know that '5 times in a row head or not, the coin is still 50% to do it again'
Try working this one, it will help keep the concept clear in your head:
You have a big batch of balls, equal amounts red, blue, and green, and the vat dumps a random ball into each of three slots and you've recorded many examples.
A) What is the probability one is red?
B) What is the probability two are red?
C) What is the probability all three are red?
D) What is the probability that all are red if you are told one of them at least is red?
This breaks out of the two-confusion but still leaves room for a three-confusion since the number of slots is the same as the number of ball colors, so you can then redo it with three ball colors but two or four slots, or you can do the original boy-girl problem but change it from two kids to three and see what changes if you are asked:
A) With 3 kids, you are told one is a boy, that are the odds one of the other two is a boy?
B) What odds both remaining kids are boys?
C) You are told two of the three kids are boys, what are the odds the remaining one is a boy?
Generally speaking a very helpful mental exercise, and were it not harder for involving larger numbers I think people would tend to solve any of those correctly more often than the real example because they'd be less likely to get hung up on the terrible twos, the problem remains the same for instance, but in some ways easier, if you are told 'for this problem, boys and girls are not equally common, and girls are born in 6 out of 10 cases'
Try working this one, it will help keep the concept clear in your head:
You have a big batch of balls, equal amounts red, blue, and green, and the vat dumps a random ball into each of three slots and you've recorded many examples.
A) What is the probability one is red?
B) What is the probability two are red?
C) What is the probability all three are red?
D) What is the probability that all are red if you are told one of them at least is red?
This breaks out of the two-confusion but still leaves room for a three-confusion since the number of slots is the same as the number of ball colors, so you can then redo it with three ball colors but two or four slots, or you can do the original boy-girl problem but change it from two kids to three and see what changes if you are asked:
A) With 3 kids, you are told one is a boy, that are the odds one of the other two is a boy?
B) What odds both remaining kids are boys?
C) You are told two of the three kids are boys, what are the odds the remaining one is a boy?
Generally speaking a very helpful mental exercise, and were it not harder for involving larger numbers I think people would tend to solve any of those correctly more often than the real example because they'd be less likely to get hung up on the terrible twos, the problem remains the same for instance, but in some ways easier, if you are told 'for this problem, boys and girls are not equally common, and girls are born in 6 out of 10 cases'
The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honors the servant and has forgotten the gift.
- Albert Einstein
King of Cairhien 20-7-2
Chancellor of the Landsraad, Archduke of Is'Mod
- Albert Einstein
King of Cairhien 20-7-2
Chancellor of the Landsraad, Archduke of Is'Mod
This message last edited by Isaac on 25/05/2010 at 04:50:03 PM
Recreational mathematics
24/05/2010 09:17:27 PM
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How is boy/girl different from girl/boy?
25/05/2010 01:05:15 AM
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I think it has to do with sequence
25/05/2010 08:37:05 AM
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The problem doesn't state the sequence, so there's no reason to assume it.
25/05/2010 08:56:09 AM
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Faulty "logic". 2/4
25/05/2010 02:12:54 AM
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I was going to say.
25/05/2010 02:48:38 AM
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Yeah
25/05/2010 05:05:16 AM
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Re: Yeah
25/05/2010 09:52:58 AM
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I don't know Python, but I think I know what went wrong there.
25/05/2010 11:33:18 AM
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Re: I don't know Python, but I think I know what went wrong there.
25/05/2010 01:53:01 PM
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Ah, I see now; sorry.
25/05/2010 02:27:05 PM
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It's also playing off your mental biases
25/05/2010 04:49:40 PM
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You realize this thread now contains the words "Monty" and "Python" several times, right?
26/05/2010 11:01:24 AM
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