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You're about to get on a plane to Seattle. You want to know if you should...

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?

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Answer #1

P(raining ) =P(at least one of the three friends is actually telling the truth)

=1-P(all three are lying) =1-(1/3)3 =1-1/27 =26/27

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