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Rain?

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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?

Feb 20, 2021

It is only raining in Seattle if all three friends are truthful. This happens with probability $$(\frac{2}{3})^3 =\boxed{\frac{8}{27}}$$