11-4 Compound Events - Math Slide Show

Lesson 11-4Objective -To find probabilities of union andintersections of two events. To use the complementto find the probability of an event.Union of A and BProbability of Compound EventsIf A and B are two events, thenP(A or B) = P(A) + P(B) −P(A and B)If A and B are mutually exclusive, thenP(A or B) = P(A) + P(B)ABIntersection of A and BIntersection of A and Bis the empty set.ABABProbability of Mutually Exclusive EventsA die is rolled one time. What is the probability ofrolling a 2 or 6?Probability of a Compound EventA die is rolled one time. What is the probability ofrolling an odd number or a prime number?P(A or B) = P(A) + P(B) = 1 6 + 1 6 = 1 3P(A or B) = P(A) + P(B) − P(A and B) = 3 6 + 3 6 − 2 6 = 2 3A card is randomly selected from a standard deckof 52 cards. What is the probability that it is a 2or a king?452 + 4 52 = 852 = 213A card is randomly selected from a standard deckof 52 cards. What is the probability that it is a redcard or a king?2652 + 452 − 2 52 = 713Algebra 2 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2010

Lesson 11-4 (cont.)Using Intersection to Find ProbabilityProbability of the Complement of an EventTwenty-five students are on the Jefferson MiddleThe event A´ (A prime), is called the complement ofSchool football team. Six of them take Algebra,event A, consists of all the outcomes that are not in A.12 of them took Biology and 15 students tookAlgebra or Biology. What is the probability thatThe probability of the complement of A isa student took both Algebra and Biology?′PA ( ) = 1 −PA( ).P(A or B) = P(A) + P(B) − P(A and B)1525 = 6 25 + 12A card is randomly selected from a standard− P(A and B)deck of 52 cards. What is the probability that it25 is not a spade?325 = P(A and B) P(not a spade) = 1 − 1352 = 3 4Events A and B are mutually exclusive.Find P(A or B).1) P(A) = 0.4P(B) = 0.50.4 + 0.5 = 0.9Algebra 2 Slide Show: Teaching Made Easy As Pi, by Mike Mills and James Wenk © 2010