Making Predictions 10-5

Vocabulary Prediction- something you can reasonably expect to happen in the future.

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.

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? Additional Example 1: Using Experimental Probability to Make Predictions Multiply the probability by the number of at bats. · 350 = x 4 10 Method 1: Set up an equation. 140 = x

Think: 4 out of 10 is how many out of 350. Method 2: Set up a proportion. The cross products are equal. Multiply. 4 · 350 = 10 · x Lawrence can predict that he will reach first base about 140 of 350 times. Additional Example 1 Continued 1400 = 10x Divide each side by 10 to isolate the variable. 140 = x = x 350

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? Check It Out: Example 1

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? Additional Example 2: Using Theoretical Probability to Make Predictions 3 · 50 = 8 · x P(spinning a 1) = 3838 Think: 3 out of 8 is how many out of = x 3838 = x 50 The cross products are equal. Multiply 150 = 8x You can expect to spin a 1 about 19 times. 8 Divide each side by 8 to isolate the variable.

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

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? Check It Out: Example 2

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? Additional Example 3: Problem Solving Application

1 Understand the Problem 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. Additional Example 3 Continued

2 Make a Plan 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. Additional Example 3 Continued

Solve 3 Additional Example 3 Continued Think: 21 out of 62 is how many out of 7. The cross products are equal. Multiply. 21 · 7 = 62 · x 7 – 2 = = x7x7 Divide each side by 62 to isolate the variable. 147 = 62x 2.37 ≈ x There will be more than 2 rainy days in 7 days. Subtract the predicted number of rainy days from the total vacation days. 62

Look Back 4 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. Additional Example 3 Continued 21 rainy days 62 total days ≈ or 33% 2.4 rainy days 7 total days ≈ 2727 or 30% Since both ratios are about 30%, the answer is reasonable.

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? Check It Out: Example 3