It's also playing of your mental biases - Edit 1
Before modification by Isaac at 25/05/2010 04:50:03 PM
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'