At a restaurant downtown, Mr. Red, Mr. Blue, Mr. Green, Mr. White and Mr. Yellow meet for lunch. Under their coats they are wearing either a red, blue, or white shirt. They are all wearing different colored shirts from their names- so that- Mr. Red is not wearing a red shirt, Mr. Blue is not wearing a blue shirt and so on.

Each of them are likely to speak truthfully with a probability of 2/3, while the chance that exactly one of them speaks falsely is 1/3.

The man wearing a red shirt says, "Mr. Red is not wearing a yellow shirt."
The man wearing a yellow shirt says, "Mr. Yellow is wearing a red shirt."

Given that exactly one of the above statement is true, determine:

(a) The probability that Mr. Green is wearing a blue shirt.
(b) The probability that Mr. Blue is wearing a white shirt.

Since we're actually told one of the statements is true and the other false, it doesn't matter what the probabilities of those events were; they happened.

Edited on October 18, 2016, 10:59 am

Posted by Charlie on 2016-10-18 10:58:05