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Warm Up

Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. Warm Up 1. Five friends form a basketball team. How many different ways could they fill the 5 positions on the team?

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Warm Up

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. Warm Up 1.Five friends form a basketball team. How many different ways could they fill the 5 positions on the team? 2.The music teacher chooses 2 of her 5 students to sing a duet. How many combinations for the duet are possible? 5!, or 120 10

  3. 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

  4. I canfind probabilities of compound events.

  5. 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.

  6. 6 2 P (pe) = = 21 7 The probability that a random two-topping order will include pepperoni is . 2 7 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

  7. 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.

  8. 1 P (o & s) = 21 The probability that a random two-topping order will include onions and sausage is . 1 21 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

  9. K L = JKL J LK = JLK JL = KJL K L J = KLJ JK = LJK L K J = LKJ 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. List permutations beginning with Jack. List permutations beginning with Kate. List permutations beginning with Linda.

  10. 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 Additional Example 2: Continued P (Kate is in the middle)

  11. K L = JKL J LK = JLK JL = KJL K L J = KLJ JK = LJK L K J = LKJ 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. List permutations beginning with Jack. List permutations beginning with Kate. List permutations beginning with Linda.

  12. 2 1 Kate lines up last P (Kate is last) = = = total number of equally likely line-ups 6 3 1 The probability that Kate lines up last is . 3 Check It Out : Example 2 (Continued)

  13. 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 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?

  14. 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 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?

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