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#1
11-02-2007, 10:53 PM
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help with math problem
this was given as extra credit, but no one in any of the classes this teacher has (highschool) got it that i know of, so wondering if we were missing something very obvious.
You have two hats, hat #1 has 8 red marbles and 2 blue marbles, hat #2 has 2 red marbles and 8 blue. you randomly select a hat and randomly choose two marbles from it, both of which are blue. you then switch hats and randomly pick out a marble, what is the probability that this will be a red marble? usually we are not allowed calculators on these extra credit problems but for this one it said a calculator was allowed and to round to the third decimal place. 
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#2
11-02-2007, 10:57 PM
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Re: help with math problem
You need to use bayes' theorem to find the probability that you selected the two blue marbles from a given hat, and then from there it is straight forward to calculate the chance that you grab a red marble from the other hat.
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#3
11-02-2007, 11:05 PM
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Re: help with math problem
[ QUOTE ]
You need to use bayes' theorem to find the probability that you selected the two blue marbles from a given hat, and then from there it is straight forward to calculate the chance that you grab a red marble from the other hat. [/ QUOTE ] i dont think any of us have heard of baye's theorem, and i dont get how the first picking affects the second
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#4
11-03-2007, 12:04 AM
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Re: help with math problem
[ QUOTE ]
[ QUOTE ] You need to use bayes' theorem to find the probability that you selected the two blue marbles from a given hat, and then from there it is straight forward to calculate the chance that you grab a red marble from the other hat. [/ QUOTE ] i dont think any of us have heard of baye's theorem, and i dont get how the first picking affects the second [/ QUOTE ] Once you pick a hat, all you know is that there's a 50% chance you have hat A, and a 50% chance you have hat B. But after you pick out two blue marbles from your first hat, you have some additional information. It should be intuitively obvious that it is now more likely that you have hat B. Bayes Theorem allows you to calculate this likelihood precisely.
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#7
11-03-2007, 02:53 AM
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Re: help with math problem
More simply put:
The chances you picked the first hat and got two blues is 1/2 x 2/10 x 1/9 or 2/180. The chances you picked the second hat and got two blues is 1/2 x 8/10 x 7/9 or 56/180. You are going to get two blues 58 out of 180 times. When you do, there is a 56 out of 58 chance it came from the second hat. So there is a 56/58 chance that you are looking at an 8/10 probability (to pick a red) and a 2/58 chance you are looking at a 2/10 probability. 56/58 x 8/10 plus 2/58 x 2/10 is 452/580.
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