Out of curiosity, here's a question from Glassdoor (Facebook Data Science Interview)
You're about to get on a plane to Seattle. You want to know if you should bring an umbrella. You call 3 random friends of yours who live there and ask each independently if it's raining. Each of your friends has a 2/3 chance of telling you the truth and a 1/3 chance of messing with you by lying. All 3 friends tell you that "Yes" it is raining. What is the probability that it's actually raining in Seattle?
Using Bayesian analysis, it's pretty clear that you cannot solve this without the prior probability of raining in Seattle.
However, here's a different approach which I found interesting in the discussion contained in Glassdoor.
Since all three friends said "Yes", the question basically boils down to what is the probability that all three friends are telling the truth given that all three friends said "Yes". Since you ask all three friends independently, the probability that all three friends are telling the truth is given by (2/3)(2/3)(2/3) = 8/27. Thus, the probability of it raining is 8/27.
While this is perhaps a bit compelling, I'm not sure if it's correct. Anyone have any ideas?