Question

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?

Answer 1

The probability that it is actually raining in Seattle is 26/27

Explanation:

Here we have the probability that a friend is telling the truth = 2/3

The probability that a friend is telling a lie = 1/3

Therefore, if all three friends say "Yes" it is raining in Seattle, the probability that is actually raining is given by the probability that one of them is telling the truth. That is the complement that all are messing with their friend.

The probability that all are not telling the truth is;

P(All not telling the truth) =
`(1)/(3) * (1)/(3) * (1)/(3) = (1)/(27)`

P(One is telling the truth) = 1 - P(All not telling the truth) =
`1- (1)/(27) = (26)/(27)`

Therefore, the probability that it is actually raining in Seattle = 26/27.