Sunshine State Standards

1. Sunshine State Standards MA.7.P.7.2 Determine, compare, and make predictions based on experimental or theoretical probability… AlsoMA.7.P.7.1

2. Vocabulary prediction

3. 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.

4. Additional Example 1: Using Experimental Probability to Make Predictions Lawrence finds that his experimental probability of getting a hit is 40%. Out of 350 at-bats, how many times can he expect to get a hit? Method 1: Set up an equation. 4 10 Multiply the probability by the number of at bats. · 350 = x 140 = x

5. 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 get a hit about 140 of 350 times.

6. Check It Out: Example 1 Marty finds the experimental probability of him making a field goal to be 74%. Out of 150 field goal attempts, how many times can he expect to make a field goal? 74 100 111 150 =

7. 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.

8. Helpful Hint Round to a whole number if it makes sense in the given situation.

9. Check It Out: Example 2 Rhonda rolls a number cube 330 times. How many times can she expect to roll a 5? x 330 1 6 ; x = 55 =

10. 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?

11. 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.

12. 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.

13. 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

14. 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.

15. Check It Out: Example 3 The Berry family is planning a 12-day vacation to a beach. The beach they have chosen averages 45 rainy days during this 109-day period. If the Berrys would like to have no rain on at least 7 days of their vacation, should they go to this spot or choose another?

16. Check It Out: Example 3 Continued 45 109 x 12 = 109x = 540 x ≈ 4.95 There will be about 5 rainy days during a 12-day period, which leaves 7 non-rainy days. The Berry family should go to this beach.

17. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

18. 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

19. 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.

20. 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

21. 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