"Most people answer “librarian.” Which is a mistake: shy salespeople are much more common than shy librarians, because salespeople in general are much more common than librarians—seventy-five times as common, in the United States."
The question is whether or not the person is more likely to be a librarian or a salesperson given that we know that they're shy. In other words, it's a posterior probability. It's a question about P(librarian|shy) vs. P(salesperson|shy). The statement that salespeople are, in general, 75 times more common than librarians is a question of prior probability, i.e. P(librarian) vs. P(salesperson).
We can easily make it be the case that the shy person is still more likely to be a librarian despite the prior probabilities given above by just saying "Assume 100% of librarians are shy and 1% of salespeople are shy." Now, given that the person is shy, the odds are 1:0.75 that they are a librarian.
Hi guys,
I'm really not happy about this claim:
"Most people answer “librarian.” Which is a mistake: shy salespeople are much more common than shy librarians, because salespeople in general are much more common than librarians—seventy-five times as common, in the United States."
The question is whether or not the person is more likely to be a librarian or a salesperson given that we know that they're shy. In other words, it's a posterior probability. It's a question about P(librarian|shy) vs. P(salesperson|shy). The statement that salespeople are, in general, 75 times more common than librarians is a question of prior probability, i.e. P(librarian) vs. P(salesperson).
We can easily make it be the case that the shy person is still more likely to be a librarian despite the prior probabilities given above by just saying "Assume 100% of librarians are shy and 1% of salespeople are shy." Now, given that the person is shy, the odds are 1:0.75 that they are a librarian.