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The probability that a climate scientist believes in MMGW  [manmade global warming] is .1; the probability that a climate scientist gets government research money is .20.  The probability that a climate scientist believes in MMGW and gets government research money is .19.  What is the probability that a climate scientist believes in MMGW given that the scientist receives government research money?

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This question is as wrong as it's politically loaded. The probability for the climate scientist to have two properties can't be higher than the probability for the climate scientist to have one of those two properties. –  joriki Feb 12 '13 at 1:48
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Hint: draw a Venn diagram and label each region with the fraction of the universe it contains. It has four regions, you have three constants plus the fact that all the regions sum to $1$.

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