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12.4 Probabilities of Compound Events Compound Event – the union or intersection of two events. Meaning the event shares something in common. Probability of Compound Events • If A and B are two events, then the probability of A or B: o “or” meaning we must decide if the events we are dealing with can occur at the same time P( A or B) = Mutually Exclusive Events: if the intersection of events A and B is empty • If A and B are mutually exclusive (meaning no intersection – the events can’t BOTH happen at the same time) then the probability of A or B: P( A or B) = Complement: of event A is denoted A’ or A consists of all outcomes that are NOT in A. Probability of the complement of an event: • P A' = P A = ( ) () Example 1: Find the indicated probability. State whether A and B are mutually exclusive. P ( A ) = 0.4 P ( B ) = 0.35 P ( A or B ) = 0.5 P ( A and B ) = ____ P ( A ) = 0.25 P ( B ) = _____ P ( A or B ) = 0.70 P ( A and B ) = 0 Example 2: A card is randomly selected from a standard deck of 52 cards. What is the probability that it is a 10 or a face card? Example 3: One six-sided die is rolled. What is the probability or rolling a multiple of a 3 or a 5? Example 4: A card is randomly selected from a standard deck of 52 cards. What is the probability that the card is a spade or a face card? Example 5: One six-sided die is rolled. What is the probability of rolling a multiple of 3 or a multiple of 2? Example 6: When two six-sided dice are tossed, there are 36 possible outcomes as shown. Find the probability of the given event. a.) The sum is NOT 8 b.) The sum is greater than or equal to 4 Example 7: A card is randomly selected from a standard deck of 52 cards. Find the probability of the given event. a.) The card is NOT a king b.) The card is not an ace or a jack. Example 8: In a poll of high school juniors, 6 out of 15 took a French class and 11 out of 15 took a math class. Fourteen out of the 15 took French or math. What is the probability that a student took both French and math? Homework: Pg 727 # 21-40, 43, 44, 46, 47