The cognitive bias presented here is to ignore the difference between P(librarian) vs P(salespeople), and draw conclusion solely based on P(shy|librarian) vs P(shy|salespeople). Since, salespeople are more likely to be shy (i.e P(shy|salespeople) > P(shy|librarian)), the bias leads to the wrong conclusion P(librarian|shy) > P(salespeople|shy).
Hi colossal_noob,
The point this example is trying to make, perhaps, can be better understood with the expansions of bayes rules.
P(librarian|shy) = (P(shy|librarian) * P(librarian)) / P(shy)
P(salespeople|shy) = (P(shy|salespeople) * P(salespeople)) / P(shy)
The cognitive bias presented here is to ignore the difference between P(librarian) vs P(salespeople), and draw conclusion solely based on P(shy|librarian) vs P(shy|salespeople). Since, salespeople are more likely to be shy (i.e P(shy|salespeople) > P(shy|librarian)), the bias leads to the wrong conclusion P(librarian|shy) > P(salespeople|shy).