Achilles is taking a test, and we want to find out how likely it is that he will pass. The probability that Achilles will study (S) is 3/5. The probability that he will pass (P) given that he studies is 4/5. The probability that he will pass the test given that he doesn't study is 1/5.
(a) What is the probability that he will pass?
(b) Assume we are told he passes the test, what is the probability that he studied given that he passed?