1. Probability of Compound Events Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. Probability of Compound Events Learn to find probabilities of compound events.

3. Probability of Compound Events 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? Additional Example 1: Using an Organized List to Find Probability 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.

4. Probability of Compound Events Pineapple – mMushroom – p Canadian bacon – p Pineapple – cMushroom – cCanadian bacon – m Pineapple – o Mushroom – o Canadian bacon – o Pineapple – peMushroom – peCanadian bacon – pe Pineapple – bMushroom – bCanadian bacon – b Pineapple – sMushroom – sCanadian bacon – s Onions – pPepperoni –p Beef – pSausage – p Onions – mPepperoni – m Beef – mSausage – m Onions – cPepperoni – cBeef – cSausage – c Onions – pePepperoni – oBeef – oSausage – o Onions – bPepperoni – bBeef – peSausage – b Onions – sPepperoni – sBeef – sSausage – pe Continued: Check It Out: Example 1 The probability that a random two-topping order will include pepperoni is. 2 7 P (pe) == 6 21 2 7

5. 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.

6. Probability of Compound Events Pineapple – mMushroom – p Canadian bacon – p Pineapple – cMushroom – cCanadian bacon – m Pineapple – o Mushroom – o Canadian bacon – o Pineapple – peMushroom – peCanadian bacon – pe Pineapple – bMushroom – bCanadian bacon – b Pineapple – sMushroom – sCanadian bacon – s Onions – pPepperoni –p Beef – pSausage – p Onions – mPepperoni – m Beef – mSausage – m Onions – cPepperoni – cBeef – cSausage – c Onions – pePepperoni – oBeef – oSausage – o Onions – bPepperoni – bBeef – peSausage – b Onions – sPepperoni – sBeef – sSausage – pe P (o & s) = 1 21 The probability that a random two-topping order will include onions and sausage is. 1 21 Continued: Check It Out: Example 1

7. Probability of Compound Events 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? Additional Example 2: Using a Tree Diagram to Find Probability Make a tree diagram showing possible line-up orders. Let J = Jack, K = Kate, and L = Linda. List permutations beginning with Jack. List permutations beginning with Kate. List permutations beginning with Linda. K  L = JKL L  K = JLK J L  J = KLJ K J  L = KJL K  J = LKJ L J  K = LJK

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

9. Probability of Compound Events Jack, Kate, and Linda line up in random order in the cafeteria. What is the probability that Kate randomly lines up last? Check It Out : Example 2 Make a tree diagram showing possible line-up orders. Let J = Jack, K = Kate, and L = Linda. List permutations beginning with Jack. List permutations beginning with Kate. List permutations beginning with Linda. K  L = JKL L  K = JLK J L  J = KLJ K J  L = KJL K  J = LKJ L J  K = LJK

10. Probability of Compound Events = 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 Check It Out : Example 2 (Continued)

11. 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? Additional Example 3: Finding the Probability of Compound Events 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

12. Probability of Compound Events Mika rolls 2 number cubes. What is the probability that the sum of the two numbers will be less than or equal to 4? Check It Out: Example 3 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