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Probability of Compound Events Warm Up Problem of the Day Lesson Presentation Lesson Quizzes Probability of Compound Events Warm Up 1. Five friends form a basketball team. How many different ways could they fill the 5 positions on the team? 5!, or 120 2. The music teacher chooses 2 of her 5 students to sing a duet. How many combinations for the duet are possible? 10 Probability of Compound Events Problem of the Day One blue sock and 7 black socks are placed in a drawer, then picked randomly one at a time without replacement. What is the probability that the blue sock is picked last? 1 8 Probability of Compound Events Learn to find probabilities of compound events. Probability of Compound Events Additional Example 1: Using an Organized List to Find Probability A pizza parlor offers seven different pizza toppings: pineapple, mushrooms, Canadian bacon, onions, pepperoni, beef, and sausage. What is the probability that a random order for a two-topping pizza includes pepperoni? Let p = pineapple, m = mushrooms, c = Canadian bacon, o = onions, pe = pepperoni, b = beef, and s = sausage. Because the order of the toppings does not matter, you can eliminate repeated pairs. Probability of Compound Events Continued: Check It Out: Example 1 Pineapple – m Pineapple – c Pineapple – o Pineapple – pe Pineapple – b Pineapple – s Mushroom – p Mushroom – c Mushroom – o Mushroom – pe Mushroom – b Mushroom – s Canadian bacon – p Canadian bacon – m Canadian bacon – o Canadian bacon – pe Canadian bacon – b Canadian bacon – s Onions – p Onions – m Onions – c Onions – pe Onions – b Onions – s Pepperoni –p Pepperoni – m Pepperoni – c Pepperoni – o Pepperoni – b Pepperoni – s Beef – p Beef – m Beef – c Beef – o Beef – pe Beef – s P (pe) = 6 = 2 Sausage – p Sausage – m Sausage – c Sausage – o Sausage – b Sausage – pe 21 7 The probability that a random two-topping order will include pepperoni is 2 . 7 Probability of Compound Events Check It Out: Example 1 A pizza parlor offers seven different pizza toppings: pineapple, mushrooms, Canadian bacon, onions, pepperoni, beef, and sausage. What is the probability that a random order for a two-topping pizza includes onion and sausage? Let p = pineapple, m = mushrooms, c = Canadian bacon, o = onions, pe = pepperoni, b = beef, and s = sausage. Because the order of the toppings does not matter, you can eliminate repeated pairs. Probability of Compound Events Continued: Check It Out: Example 1 Pineapple – m Pineapple – c Pineapple – o Pineapple – pe Pineapple – b Pineapple – s Mushroom – p Mushroom – c Mushroom – o Mushroom – pe Mushroom – b Mushroom – s Canadian bacon – p Canadian bacon – m Canadian bacon – o Canadian bacon – pe Canadian bacon – b Canadian bacon – s Onions – p Onions – m Onions – c Onions – pe Onions – b Onions – s Pepperoni –p Pepperoni – m Pepperoni – c Pepperoni – o Pepperoni – b Pepperoni – s Beef – p Beef – m Beef – c Beef – o Beef – pe Beef – s P (o & s) = 1 Sausage – p Sausage – m Sausage – c Sausage – o Sausage – b Sausage – pe 21 The probability that a random two-topping order will include onions and sausage is 1 . 21 Probability of Compound Events Additional Example 2: Using a Tree Diagram to Find Probability Jack, Kate, and Linda line up in random order in the cafeteria. What is the probability that Kate randomly lines up between Jack and Linda? Make a tree diagram showing possible line-up orders. Let J = Jack, K = Kate, and L = Linda. J K L = JKL L K = JLK List permutations beginning with Jack. K J L = KJL L J = KLJ List permutations beginning with Kate. L J K = LJK K J = LKJ List permutations beginning with Linda. Probability of Compound Events Additional Example 2: Continued P (Kate is in the middle) Kate lines up in the middle 2 1 = = = total number of equally likely line-ups 6 3 The probability that Kate lines up between Jack and Linda is 1 . 3 Probability of Compound Events Check It Out : Example 2 Jack, Kate, and Linda line up in random order in the cafeteria. What is the probability that Kate randomly lines up last? Make a tree diagram showing possible line-up orders. Let J = Jack, K = Kate, and L = Linda. J K L = JKL L K = JLK List permutations beginning with Jack. K J L = KJL L J = KLJ List permutations beginning with Kate. L J K = LJK K J = LKJ List permutations beginning with Linda. Probability of Compound Events Check It Out : Example 2 (Continued) P (Kate is last) = 2 1 Kate lines up last = = total number of equally likely line-ups 6 3 The probability that Kate lines up last is 1 3 . Probability of Compound Events Additional Example 3: Finding the Probability of Compound Events Mika rolls 2 number cubes. What is the probability that the sum of the two numbers will be less than 4? There are 3 out of 36 possible outcomes that have a sum less than 4. 1 The probability of rolling a sum less than 4 is . 12 Probability of Compound Events Check It Out: Example 3 Mika rolls 2 number cubes. What is the probability that the sum of the two numbers will be less than or equal to 4? There are 6 out of 36 possible outcomes that have a sum less than or equal to 4. 1 The probability of rolling a sum less than or equal to 4 is . 6 Probability of Compound Events Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems Probability of Compound Events Lesson Quiz 1. The teacher randomly chooses two school days each week to give quizzes. What is the probability that he or she chooses Monday and Wednesday? 1 10 2. A bag contains three red checkers and three black checkers. Two checkers are randomly pulled out. What is the probability that 1 red checker and 1 black checker are chosen? 3 5 3. A baseball video game randomly assigns positions to 9 players. What is the probability that Lou, Manny, and Neil will be randomly 1 selected for the three-member outfield? 84 Probability of Compound Events Lesson Quiz for Student Response Systems 1. Two number cubes are rolled. What is the probability that the sum of the two numbers will be 1? A. 0 B. 1 1 C. 6 1 D. 36 Probability of Compound Events Lesson Quiz for Student Response Systems 2. Two number cubes are rolled. What is the probability that the sum of the two numbers will be 6? A. 0 B. 1 1 C. 6 1 D. 36 Probability of Compound Events Lesson Quiz for Student Response Systems 3. Two number cubes are rolled. What is the probability that the sum of the two numbers will be 11? A. 0 B. 1 1 6 D. 1 36 C.