Puzzle | Is it Raining

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?

Answer: 26/27


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.

My Personal Notes arrow_drop_up

BTech Computer Science student at IIIT Vadodara

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