You’re about to get on a plane to Seattle. You want to know if it’s raining. You call 3 random friends who live there and ask each if it’s raining. Each friend 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?
+1223 It is only raining in Seattle if all three friends are truthful. This happens with probability \((\frac{2}{3})^3 =\boxed{\frac{8}{27}}\)
