Suppose that 10% of athletes in a competition are cheating by taking banned stimulants. A test is available that yields evidence of cheating (i.e. a positive test) 8% of the time for athletes who are not cheating and 70% of the time for athletes who are cheating.

(a) What is the probability of a randomly selected athlete testing positive?

(b) If an athlete tests positive what is the probability they were cheating?