Suppose that the referee for a football game has two coins that look the same, except that one of them is fair and the other is weighted to fall heads with probability .85. The referee doesn't know which is which, and decides to select one of them and ?ip it 20 times and if it lands heads 17 times or more then the referee will designate that coin as the weighted one.
a) If the coin the referee selects is fair, what is the probability that it gets designated as being weighted?
b) If the coin is weighted, what is the probability that the test designates it as being weighted?