13. 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?
They all told 'yes' which mean either all of them are telling truth or all of them are lying. Probability of all of them telling the truth is 8/27 and probability of all of them are lying is 1/27 which means that out of all the 27 possible cases only 9 are applicable here. Out of those 9, 8 are of telling truth, so answer would be 8/9.
It's just my guess, i don't know if it is correct.