Probability Theorem: Let E and F be two events in a sample space. (a) The probability of event E or F occurring p(EUF) = p(E) +p(F) p(E^F). (b) If E and F are mutually exclusive (disjoint), then p(EU F) = p(E) +p(F). (c) If E is the complementary event of E, then p(E) = 1 p(E). (d) If an event E of S consists of an event E in S, followed by an event E2 in S2, followed by an event E3 in S3, and so on, then p(E) = p(E) p(E2) p(En). Examples Remark: We want to use the Probability Theorem above when computing probabilities given as decimals. Here is an example. Suppose a baseball player has a batting average of .250. This means he gets at hit (H) 25% of the time and does not get a hit (N) 75% of the time. Suppose that in a certain game, this player is at bat 5 times. 1. What is the probability he will get exactly three hits in the game? 2. What is the probability he will get at least one hit in the game?