ABCDEFGHIJKLMNOPQRSTUVWX
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Problem
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Mark is a thin man from Germany with glasses who likes to listen to Mozart. Which is more likely? That Mark is A) a truck driver or (B) a professor of literature in Frankfurt?
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From: The Art of Thinking Clearly, Rolf Dobelli
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STEP 1: Create estimates
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Professors (πŸ§‘β€πŸ«) who fit the description (πŸ‘“)Truck drivers (πŸš›) who fit the description (πŸ‘“)
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25%
of professors who wear glasses and fit the description
0.2%
of truck drivers who wear glasses and fit the description
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0.0002%
of people in Germany who are professors of literature in Frankfurt
0.1%
of people in Germany who are truck drivers
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0.2%
of people in Germany who wear glasses and fit the description
0.2%
of people in Germany who wear glasses and fit the description
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STEP 2: Add the estimates to the contingency table
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Contingency table: p(πŸ§‘β€πŸ«) x p(πŸ‘“)Contingency table: p(πŸš›) x p(πŸ‘“)
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πŸ‘“NOTMargin
(total counts)		πŸ‘“NOTMargin
(total counts)
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πŸ‘“πŸ‘“
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πŸ§‘β€πŸ«43170πŸš›17085,000
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(25% of 170)(0.00002% of 85m)(0.2% of 85,000)(0.1% of 85m)
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NOT πŸ§‘β€πŸ«NOT πŸš›
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Margin
(total counts) 		170,00085,000,000Margin
(total counts) 		170,00085,000,000
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(0.2% of 85m)(German population)(0.2% of 85m)(German population)
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STEP 3: Calculate the blanks (all rows and columns should sum to their margins)
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Contingency table: p(πŸ§‘β€πŸ«) x p(πŸ‘“)Contingency table: p(πŸš›) x p(πŸ‘“)
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πŸ‘“NOTMargin
(total counts)		πŸ‘“NOTMargin
(total counts)
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πŸ‘“πŸ‘“
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πŸ§‘β€πŸ«43128170πŸš›17084,83085,000
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(25% of 170)(0.00002% of 85m)(0.2% of 85,000)(0.1% of 85m)
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NOT πŸ§‘β€πŸ«169,95884,829,87384,999,830NOT πŸš›169,83084,745,17084,915,000
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Margin
(total counts) 		170,00084,829,74585,000,000Margin
(total counts) 		170,00084,660,34085,000,000
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(0.2% of 85m)(German population)(0.2% of 85m)(German population)
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STEP 4: Calculate the probabilities
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ProbabilityCalculationProbabilityCalculation
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p(πŸ‘“ | πŸ§‘β€πŸ«)0.25000043 / (43 + 128)p(πŸ‘“ | πŸš›)0.002000170 / (170 + 84,830)
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p(πŸ‘“)0.002000170,000 / 85,000,000p(πŸ‘“)0.002000170,000 / 85,000,000
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p(πŸ§‘β€πŸ« | πŸ‘“)0.00025043 / (43 + 169,958)p(πŸš› | πŸ‘“)0.001000170 / (170 + 169,830)
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p(πŸ§‘β€πŸ«)0.000002170 / 85,000,000p(πŸš›)0.00100085,000 / 85,000,000
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STEP 5: Finalise inferences
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400%
greater likelihood of πŸš› fitting the description (πŸ‘“) vs πŸ§‘β€πŸ«fitting the description
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12500%
greater likelihood of the description (πŸ‘“) fitting πŸ§‘β€πŸ« vs fitting πŸš›
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Conclusion:
Despite the Frankfurt literature professors being x125 more likely than truck drives to fit the description, a person with the description is x4 more likely to be a trick driver than a professor.
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