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## Warm Up

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**Warm Up**Problem of the Day Lesson Presentation Lesson Quizzes**Warm Up**Solve each proportion. 1. Which represents a greater amount–0.04 or 3.9 percent? 2. A bag contains 9 lettered tiles. There are 5 Es, 3 Ts, and 1 X. What letter would you be most likely to draw? 0.04 An E**Problem of the Day**After several tries, Carla figures that the probability of her flipping a playing card into a hat is . If she was successful on 3 tries, how many times did she miss? 1 8 21**Vocabulary**prediction**A prediction is something you can reasonably expect to**happen in the future. Weather forecasters use several different methods of forecasting to make predictions about the weather. One way to make a prediction is to use probability.**Additional Example 1: Using Experimental Probability to Make**Predictions Lawrence finds the experimental probability of his reaching first base is 40%. Out of 350 at-bats, how many times can he expect to reach first base? Method 1: Set up an equation. 4 10 Multiply the probability by the number of at bats. · 350 = x 140 = x**x 350**4 10 = Additional Example 1 Continued Method 2: Set up a proportion. Think: 4 out of 10 is how many out of 350. The cross products are equal. 4 · 350 = 10 · x Multiply. 1400 = 10x Divide each side by 10 to isolate the variable. 10 10 140 = x Lawrence can predict that he will reach first base about 140 of 350 times.**Check It Out: Example 1**Malia finds the experimental probability of her scoring a goal is 20%. Out of 225 attempts, how many times can she expect to score a goal? Method 1: Set up an equation. 2 10 Multiply the probability by the number of attempts. · 225 = x 45 = x**x 225**2 10 = Check It Out: Example 1 Continued Method 2: Set up a proportion. Think: 2 out of 10 is how many out of 225. The cross products are equal. 2 · 225 = 10 · x Multiply. 450 = 10x Divide each side by 10 to isolate the variable. 10 10 45 = x Malia can predict that she will score about 45 goals of 225 attempts.**3 8**x 50 = Additional Example 2: Using Theoretical Probability to Make Predictions A spinner has eight sections of equal size. Three sections are labeled 1, two are labeled 2, and the others are labeled 3, 4, and 5. In 50 spins, how often can you expect to spin a 1? 3 8 P(spinning a 1) = Think: 3 out of 8 is how many out of 50. 3 · 50 = 8 · x The cross products are equal. Multiply 150 = 8x Divide each side by 8 to isolate the variable. 8 8 18.75 = x You can expect to spin a 1 about 19 times.**Helpful Hint**Round to a whole number if it makes sense in the given situation.**2 8**x 50 = Check It Out: Example 2 A spinner has eight sections of equal size. Three sections are labeled 1, two are labeled 2, and the others are labeled 3, 4, and 5. In 50 spins, how often can you expect to spin a 2? 2 8 P(spinning a 2) = Think: 2 out of 8 is how many out of 50. 2 · 50 = 8 · x The cross products are equal. 100 = 8x Multiply. Divide each side by 8 to isolate the variable. 8 8 You can expect to spin a 2 about 13 times. 12.5 = x**Additional Example 3: Problem Solving Application**The Singh family is planning a 7-day tropical vacation during July or August. The island destination they have chosen averages 21 rainy days during this 62-day period. If the Singhs would like to avoid rain on at least 5 days of their vacation, should they go to this spot or choose another?**1**Understand the Problem Additional Example 3 Continued The answer will be whether the Singh family should go to the island. List the important information: • The island destination averages 21 rainy days out of 62 days. • The Singhs want to avoid rain on at least 5 days of their vacation.**2**Make a Plan Additional Example 3 Continued On average 21 out of the 62 days it is rainy. After finding out the number of rainy days there should be forecast, subtract to find the number of not rainy days.**3**Solve Additional Example 3 Continued x 7 21 62 Think: 21 out of 62 is how many out of 7. = The cross products are equal. 21 · 7 = 62 · x 147 = 62x Multiply. Divide each side by 62 to isolate the variable. 62 62 There will be more than 2 rainy days in 7 days. 2.37 ≈ x Subtract the predicted number of rainy days from the total vacation days. 7 – 2 = 5**4**21 rainy days 62 total days 20 60 ≈ or 33% 2.4 rainy days 7 total days 2 7 ≈ or 30% Additional Example 3 Continued Look Back They should choose a different location. It is likely to rain more than 2 days (about 2.4 days) during a 7-day period, which will not give the Singhs at least 5 sunny days. Since both ratios are about 30%, the answer is reasonable.**Check It Out: Example 3**The Reid family is planning a 9-day winter vacation during December or January. The destination they have chosen averages 35 snow days during this 60-day period. If the Reids would like to avoid snow on at least 4 days of their vacation, should they go to this spot or choose another?**1**Understand the Problem Check It Out: Example 3 Continued The answer will be whether the Reid family should go to the destination. List the important information: • The destination averages 35 snow days out of 60 days. • The Reids want to avoid snow on at least 4 days of their vacation.**2**Make a Plan Check It Out: Example 3 Continued On average 35 out of the 60 days it is snowing. After finding out the number of snow days there should be forecast, subtract to find the number of not snow days.**3**Solve x 9 35 60 = Check It Out: Example 3 Continued Think: 35 out of 60 is how many out of 9. The cross products are equal. 35 · 9 = 60 · x 315 = 60x Multiply. Divide each side by 60 to isolate the variable. 60 60 There will be more than 5 snow days in 9 days. 5.25 = x Subtract the predicted number of snow days from the total vacation days. 9 – 5 = 4**4**35 snow days 60 total days 35 60 ≈ or 58% 5.25 snow days 9 total days 5 9 ≈ or 55% Check It Out: Example 3 Continued Look Back They should choose a different location. It is likely to snow more than 5 days during a 9-day period, which will not give the Reids at least 4 days without snow. Since both ratios are about 55%, the answer is reasonable.**Lesson Quizzes**Standard Lesson Quiz Lesson Quiz for Student Response Systems**Lesson Quiz: Part I**1. The experimental probability of Maura shooting a goal in field hockey is 12%. Out of 300 shots, how many can Maura predict will be goals? 2. If Scott flips two quarters 25 times, how many times can he expect to flip two heads? 32 6 times**Lesson Quiz: Part II**3. The Aurelio family is planning a 12-day skiing trip during December or january. The region they have chosen gets the right conditions for skiing 46 days during the 62-day period. The Aurelios would like to spend at least 8 days skiing. Will their destination be a good choice? Yes. There will be at least 8 days with the right conditions for skiing.**Lesson Quiz for Student Response Systems**1. Katia finds the probabilty that the traffic light is red when she reaches an intersection is 45%. In one month, she goes through the intersection 65 times. How many times can she expect the light to be red when she reaches the intersection? A. 22 B. 26 C. 30 D. 45**Lesson Quiz for Student Response Systems**2. If you roll a number cube 12 times, about how many times do you expect to roll a number less than five? A. 6 B. 8 C. 10 D. 12