A Geek is about to get a plane to Hyderabad. Geek wants to know if it’s raining. Geek calls 3 random friends staying at Hyderabad to ask this question. Each friend has a 2/3 chance of telling the truth and 1/3 chance of lying. All the three friends gave the response as “Yes, it is Raining”.
Q. What is the probability that it’s actually raining in Hyderabad?
The Geek only requires one of the friends to be telling the truth.
The probability that at least one of them is telling the truth will be:
1 - (Probability that all of them Lied)
The probability that all of them lied is 1/27. i.e. 1/3 * 1/3 * 1/3
So, now the probability that at least one of them told the truth is: 1 – (1/27) = 26/27.
So, it is approximately 96% that it is raining in Hyderabad.
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