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## Main Question or Discussion Point

Dear Probability subforum,

I have hard time thinking through how 11% is calculated. Anyone have any ideas? From "Thinking fast and slow" Kahneman. p 154

"...If you believe 3% of graduate students are enrolled in computer science (the base rate), and you also believe that the description of Tom W is 4 times more likely for a graduate student in that field than in other fields, then Bayes's rule says you must believe that the probability that Tom W is a computer scientist is now 11%. If the base rate had been 80%, the new degree of belief would be 94.1%. And so on...."

Description of Tom W is that of typical CS student.

I have hard time thinking through how 11% is calculated. Anyone have any ideas? From "Thinking fast and slow" Kahneman. p 154

"...If you believe 3% of graduate students are enrolled in computer science (the base rate), and you also believe that the description of Tom W is 4 times more likely for a graduate student in that field than in other fields, then Bayes's rule says you must believe that the probability that Tom W is a computer scientist is now 11%. If the base rate had been 80%, the new degree of belief would be 94.1%. And so on...."

Description of Tom W is that of typical CS student.