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?

ANSWER 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? ANSWER 1 8

Learn to find probabilities of compound events. I will… Learn to find probabilities of compound events.

Using an Organized List to Find Probability 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.

Continued: Check It Out: Example 1 Pineapple – m Mushroom – p Canadian bacon – p Pineapple – c Mushroom – c Canadian bacon – m Pineapple – o Mushroom – o Canadian bacon – o Pineapple – pe Mushroom – pe Canadian bacon – pe Pineapple – b Mushroom – b Canadian bacon – b Pineapple – s Mushroom – s Canadian bacon – s Onions – p Pepperoni –p Beef – p Sausage – p Onions – m Pepperoni – m Beef – m Sausage – m Onions – c Pepperoni – c Beef – c Sausage – c Onions – pe Pepperoni – o Beef – o Sausage – o Onions – b Pepperoni – b Beef – pe Sausage – b Onions – s Pepperoni – s Beef – s Sausage – pe The probability that a random two-topping order will include pepperoni is . 2 7 P (pe) = = 6 21 5

Practice 1 – Use 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.

Continued Practice 1 1 P (o & s) = 21 Pineapple – m Mushroom – p Canadian bacon – p Pineapple – c Mushroom – c Canadian bacon – m Pineapple – o Mushroom – o Canadian bacon – o Pineapple – pe Mushroom – pe Canadian bacon – pe Pineapple – b Mushroom – b Canadian bacon – b Pineapple – s Mushroom – s Canadian bacon – s Onions – p Pepperoni –p Beef – p Sausage – p Onions – m Pepperoni – m Beef – m Sausage – m Onions – c Pepperoni – c Beef – c Sausage – c Onions – pe Pepperoni – o Beef – o Sausage – o Onions – b Pepperoni – b Beef – pe Sausage – b Onions – s Pepperoni – s Beef – s Sausage – pe P (o & s) = 1 21 The probability that a random two-topping order will include onions and sausage is .

Using a Tree Diagram to Find Probability 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. K  L = JKL L  K = JLK J List permutations beginning with Jack. L  J = KLJ K J  L = KJL List permutations beginning with Kate. K  J = LKJ L J  K = LJK List permutations beginning with Linda.

Continued Example 2 P (Kate is in the middle) = Kate lines up in the middle total number of equally likely line-ups 2 6 1 3 The probability that Kate lines up between Jack and Linda is . 1 3

Practice 2 – Using 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. K  L = JKL L  K = JLK J List permutations beginning with Jack. L  J = KLJ K J  L = KJL List permutations beginning with Kate. K  J = LKJ L J  K = LJK List permutations beginning with Linda.

The probability that Kate lines up last is . 1 Continued Practice 2 = P (Kate is last) Kate lines up last total number of equally likely line-ups 2 6 1 3 The probability that Kate lines up last is . 1 3

Finding the Probability of Compound Events 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. The probability of rolling a sum less than 4 is . 1 12

Practice 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. The probability of rolling a sum less than or equal to 4 is . 1 6

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 14 14 14 14

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? 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. A baseball video game randomly assigns positions to 9 players. What is the probability that Lou, Manny, and Neil will be randomly selected for the three-member outfield?

ANSWERS 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? 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. A baseball video game randomly assigns positions to 9 players. What is the probability that Lou, Manny, and Neil will be randomly selected for the three-member outfield? 1 10 3 5 1 84

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. B. C. D. 1 17 17 17 17

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 C. D. 18 18 18 18

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 C. D. 19 19 19 19