10 5 Making Predictions Learn to use probability

10 -5 Making Predictions Learn to use probability to predict events.

10 -5 Making Predictions 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.

10 -5 Making Predictions Example A Caitlyn finds that the experimental probability of her making a three-point shot is 30%. Out of 500 three-point shots, about how many could she predict she would make? P(three-point shot) = 30 Write probability as a fraction. 100 30 = X Think: 30 out of 100 is how 100 500 many out of 500. 15000=100 x 150 = x You can expect Caitlyn to make 150 three-point shots

10 -5 Making Predictions Helpful Hint Round to a whole number if it makes sense in the given situation.

10 -5 Making Predictions Example B A spinner has eight sections of equal size. Three sections are labelled 1, two are labelled 2, and the others are labelled 3, 4, and 5. In 50 spins, how often can you expect to spin a 2? 2 P(spinning a 2) = 8 2 x Think: 2 out of 8 is how many = 8 50 out of 50. 100 = 8 x 12. 5 = x You can expect to spin a 2 about 13 times.

10 -5 Making Predictions YOU TRY 1 West Palm Beach, Florida, gets rain about 16% of the time. On how many days out of 400 can residents of West Palm Beach predict they will see rain? West Palm Beach residents can expect 64 days of rain.

10 -5 Making Predictions YOU TRY 2 If you roll a number cube 12 times, about how many times do you expect to roll a number less than five? You can expect to roll a number less than five 8 times.

10 -5 Making Predictions Example C The Wettermark family is planning a 14 -day vacation. They would like to go to Pensacola, Florida, sometime in July, August, or September. Pensacola averages 19 rainy days during those 92 days. If the Wettermarks would like no rain on at least 10 days of their vacation, should they go to Pensacola?

10 -5 Making Predictions x 19 = 14 92 Example C continued Think: 19 out of 92 is how many out of 14. 266 = 92 x 2. 89 ≈ x There will be about 3 rainy days in 14 days. 14 – 3 = 11 Subtract the predicted number of rainy days from the total vacation days. Since 11>10, the Wettermarks can reasonably expect at least 10 not rainy days on their vacation and should go to Pensacola.

10 -5 Making Predictions YOU TRY The Arno family is planning a 14 - day April vacation. The location they’ve chosen has 10 rainy days in April. The Arnos would like at least 7 days without rain. Should they keep their current plans? Explain.

10 -5 Making Predictions x 10 = 14 30 YOU TRY continued Think: 10 out of 30 is how many out of 14. 140 = 30 x 4. 67 = x There will be about 5 rainy days in 14 days. 14 – 5 = 9 Subtract the predicted number of rainy days from the total vacation days. Yes, they should keep their plans. The location is likely to provide over 9 days without rain.

10 -5 Making Predictions 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? 32 2. If Scott flips two quarters 25 times, how many times can he expect to flip two heads? 6 times

10 -5 Making Predictions 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.

10 -5 Making Predictions 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