Base rate probability application question

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SELFMADE
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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.
 

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Hey SELFMADE.

So in this problem you have two events: the belief of someone being a student and the event that they actually are a student. We call these events A and B and they are both binary variables (i.e. true or false).

So you have the probabilities P(A|B) and P(B|A) and what you want to do is given P(A|B), you want to find the reverse of P(B|A).

Since there are many examples on the internet of this, I'll just post a link to the first one google showed that is relevant:

http://www.johndcook.com/rarediseases.pdf