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Over Lesson 13–7 1) What is the probability of getting a 7 while rolling two number cubes? 2) What is the probability of rolling an odd number when rolling two number cubes? Over Lesson 13-6

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Splash Screen

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Then/Now You have already found the probability of simple events. (Lesson 13–6) Use tree diagrams or the Fundamental Counting Principle to count outcomes. Use tree diagrams or the Fundamental Counting Principle to find the probability of an event.

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Vocabulary tree diagrams Fundamental Counting Principle A diagram used to show the total number of possible outcomes. If there are two events that occur separately from each other, the way they occur together is their product (example: if I have five shirts and three pants, I have 5 3 or 15 different potential outfits)

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Example 1 Use a Tree Diagram to Count Outcomes GREETING CARDS A greeting card maker offers three birthday greetings in four possible colors, as shown below. Draw a tree diagram to find the number of cards that can be made from three greeting choices and four color choices.

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Example 1 Use a Tree Diagram to Count Outcomes You can draw a diagram to find the number of possible cards. Answer: There are 12 possible cards.

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A.A B.B C.C D.D Example 1 CYP A.3 B.5 C.8 D.15 ICE CREAM An ice cream parlor offers a special on one-scoop sundaes with one topping. The ice cream parlor has 5 different flavors of ice cream and three different choices for toppings. How many different sundaes can be made?

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Concept

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Example 2 Use the Fundamental Counting Principle CELL PHONES A cell phone company offers 3 payment plans, 4 styles of phones, and 6 decorative phone wraps. How many phone options are available? Use the Fundamental Counting Principle. The number of types of payment plans times the number of styles of phones times the number of decorative wrapsequals the number of possible outcomes. 3×4 ×6=72 Answer:There are 72 possible phone options.

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A.A B.B C.C D.D Example 2 CYP A.60 B.12 C.5 D.3 SANDWICHES A sandwich shop offers 4 choices for bread, 5 choices for meat, and 3 choices for cheese. If a customer can make one choice from each category, how many different sandwiches can be made?

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Example 3 Find Probabilities TOYS A toy robot moves straight ahead until it hits an obstacle. Then it turns, with equal chances of turning left or right. If the robot makes three turns, what is the probability that all three will be left turns? First, find the number of outcomes the robot can move with a tree diagram.

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Example 3 Find Probabilities There are 8 outcomes. Only one of them is left, left, left.

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A.A B.B C.C D.D Example 3 CYP A Abigail tosses a number cube 3 times. What is the probability that she will toss a 2 each time? A. B. C. D.

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Example 4 Find Probabilities Henry rolls a number cube and tosses a coin. What is the probability that he will roll a 3 and toss heads? Step 1First, find the number of outcomes. 123456123456Number Cube HTHTHTHTHTHTHTHTHTHTHTHTCoin There are 12 possible outcomes.

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Example 4 Find Probabilities Step 2Find the probability. Look at the tree diagram. There is one outcome that has a 3 and a head.

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A.A B.B C.C D.D Example 4 CYP Bob rolls a number cube and tosses a coin. What is the probability that he will roll an odd number and toss tails? A. B. C. D.1

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End of the Lesson

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