There is a new diagnostic test for a disease that occurs in about 0.05% of the population. the test is not perfect, but will detect a person with the disease 99% of the time. it will, however, say that a person without the disease has the disease about 3% of the time. a person is selected at random from the population, and the test indicates that this person has the disease. what are the conditional probabilities that(a) the person has the disease? (b) the person does not have the disease?

Our star pitcher, foster enlight, can throw a pitch so fast that it gets to the catcher’s mitt before it leaves foster’s fingers! if the team wins a game then the probability that foster was pitching is 0.8 but only if foster had at least one day’s rest since his last pitching assignment. if foster does not have a day off and the team still wins, the probability that foster was pitching drops by half of what it was on the previous day. if the team wins three games in succession from the toronto tachyons and foster pitched in game #2, what is the probability that he pitched in one or more of the other games? (assume that foster did not pitch on the day before the first game of this three game series.)