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?
As all three friends said Yes so either all of them are telling truth or all are lying.
case 1: All telling truth 2/3*2/3*2/3 = 8/27
case 2: All lying 1/3 * 1/3 * 1/3 = 1/27
case 1 is favourable to raining and case 2 is against it
so probability that it is raining in Hyderabad is (8/27)/(8/27 + 1/27) = 8/9
So, it is approximately 89% chance that it is raining in Hyderabad.