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10-6 Making Decisions and Predictions Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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Warm Up Solve each proportion. 1. =2. = 3. =4. = Course Making Decisions and Predictions n9n9 x n x

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Problem of the Day Aiden is playing a board game using two six-sided number cubes. He wins if he doesn’t roll a six or a seven. What is the probability that Aiden will win on his next turn? Course Making Decisions and Predictions

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Learn to use probability to make decisions and predictions. Course Making Decisions and Predictions

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The table shows the satisfaction rating in a business’s survey of 500 customers. Of their 240,000 customers, how many should the business expect to be unsatisfied? Additional Example 1A: Using Probability to Make Decisions and Predictions number of customers unsatisfied in survey total number of customers surveyed Course Making Decisions and Predictions PleasedSatisfiedUnsatisfied Find the probability of unsatisfied customers in the survey. = or 7 100

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Additional Example 1A Continued Course Making Decisions and Predictions Set up a proportion. = t n t 240,000 7 x 240,000 = 100n Find the cross products. Divide both sides by ,680,000 = 100n t ,800 = n The business should expect to have 16,800 unsatisfied customers.

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Jared randomly draws a card from a 52-card deck and tries to guess what it is. If he tried this trick 1040 times over the course of his life, what is the best prediction for the amount of times it works? Additional Example 1B: Using Probability to Make Decisions and Predictions number of possible outcomes total possible outcomes Course Making Decisions and Predictions Find the theoretical probability of successful trick attempts. = 1 52

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Additional Example 1B Continued 1 52 Course Making Decisions and Predictions Set up a proportion. = t n t 1040 = 52n Find the cross products. Divide both sides by = 52n t = n The trick would work about 20 times.

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The table shows the satisfaction rating in a business’s survey of 500 customers. Of their 240,000 customers, how many should the business expect to be pleased? Check It Out: Example 1A number of customers pleased in survey total number of customers surveyed Course Making Decisions and Predictions PleasedSatisfiedUnsatisfied Find the probability of pleased customers in the survey. = or 1414

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Check It Out: Example 1A Continued 1414 Course Making Decisions and Predictions Set up a proportion. = t n t 240,000 1 240,000 = 4n Find the cross products. Divide both sides by ,000 = 4n t ,000 = n The business should expect to have 60,000 please customers.

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Kaitlyn randomly draws a domino tile from an 18 piece set and tries to guess what it is. If she tries this trick 2250 times over the course of her life, what is the best prediction for the amount of times it works? Check It Out: Example 1B number of possible outcomes total possible outcomes Course Making Decisions and Predictions Find the theoretical probability of successful trick attempts. = 1 18

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Check It Out: Example 1B Continued 1 18 Course Making Decisions and Predictions Set up a proportion. = t n t x 2250 = 18n Find the cross products. Divide both sides by = 18n t = n Approximately 125 times the trick would work.

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In a game, two players each flip a coin. Player A wins if exactly one of the two coins is heads. Otherwise, player B wins. Determine whether the game is fair. Additional Example 2: Deciding Whether a Game is Fair P(player A winning) = Course Making Decisions and Predictions List all possible outcomes. Find the theoretical probability of each player’s winning HH HT TT TH P(player B winning) = There are 2 possibilities with exactly 1 coin as heads Since =, the game is fair

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In a new game, two players each flip a coin. Player A wins if at least one of the two coins is heads. Otherwise, player B wins. Determine whether the game is fair. Check It Out: Example 2 P(player A winning) = Course Making Decisions and Predictions List all possible outcomes. Find the theoretical probability of each player’s winning HH HT TT TH P(player B winning) = There are 3 possibilities with at least 1 coin as heads Since ≠, the game is not fair

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Lesson Quiz: Part I 1. Out of the 35 products a salesperson sold last week, 8 of them were products worth over $200. About how many of these products should the salesperson expect to sell if he has 140 customers next month? 2. A student answers all 12 multiple choice questions on a quiz at random. Each multiple choice question has 4 choices. What is the best guess for the amount of multiple choice questions the student will answer correctly? 3 32 Insert Lesson Title Here Course Making Decisions and Predictions

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Lesson Quiz: Part II 3. In a game, two players each roll a 6-sided number cube and add the two numbers. If the roll is a 6 or less, player A wins. If the roll is 8 or more, player B wins. if the roll is a 7, the players tie and roll again. Is this a fair game? Yes Insert Lesson Title Here Course Making Decisions and Predictions

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