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Lesson 10.4 Probability of Disjoint and Overlapping Events Learning Goal: (S-CP.A.1 and S-CP.B.7) I can use the Addition Rule to find probabilities of disjoint (mutually exclusive) and overlapping events. Essential Question: How can you find probabilities of disjoint mutually exclusive and overlapping events? Homework Discussion c. 89% d. not ind c. 21% d. ind Exploration A six-sided die is rolled. Draw a Venn Diagram that relates the two events. Venn Diagram 1. Event A: The result is an even number. Event B: The result is a prime number. Are the events disjoint or overlapping? P(A) = P(B) = P(A and B) = P(A or B) = P(A ∩ B) P(A U B) Venn Diagram 2. Event A: The result is 2 or 4. Event B: The result is an odd number. Are the events disjoint or overlapping? P(A) = P(B) = P(A and B) = P(A or B) = P(A ∩ B) P(A U B) In general, if event A and event B are disjoint, then what is the probability that event A or event B will occur? In general, if event A and event B are overlapping, then what is the probability that event A or event B will occur? Probabilities of Compound Events Compound Events: the union or intersection of two events Disjoint (Mutually Exclusive) Events: no outcomes in common Overlapping Events: one or more outcomes in common Match the word to the diagram that it represents Union Intersection Disjoint Union Intersection Disjoint Overlapping Overlapping Probabilities of Compound Events P(A or B) = P(A) + P(B) - P(A and B) If the two events are disjoint (mutually exclusive) then: P(A or B) = P(A) + P(B) Why? Example: A card is randomly selected from a standard deck of 52 playing cards. What is the probability that it is a 10 or a face card? Step 1: Disjoint or Overlapping? 4 suits (2 red, 2 black) Why? Step 2: Determine the events. Event A: card is a 10 Event B: face card 13 cards per suit 3 face cards per suit Step 3: Find the probabilities. P(A) = P(B) = P(A or B) = Example 2: A bag contains cards numbered 1 through 20. One card is randomly selected. What is the probability that the number on the card is a multiple of 3 or a multiple of 4? Step 1: Step 3: Step 2: Group Consensus Even Groups: A card is randomly selected from a standard deck of 52 playing cards. What is the probability that it is a face card or a spade? Odd Groups: Two six-sided dice are rolled. What is the probability that the sum of the numbers rolled is a multiple of 4 or is 5? Example 3: Out of 200 students in a senior class, 113 students are either varsity athletes or on the honor roll. There are 74 seniors who are varsity athletes and 51 seniors who are on the honor roll. What is the probability that a randomly selected senior is both a varsity athlete and on the honor roll? Step 1: Disjoint or Overlapping Step 2: Determine Events Event A: Step 3: Find the Probabilities P(A) = P(A and B) = P(B) = Event B: P(A or B) = Exit Problem: Practice to Strengthen Understanding Hmwk # 19 BI p567 #1-15