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: 8/9
Explanation:
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.