10-5 Making Predictions
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
10-5 Making Predictions
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?An E
0.04
10-5 Making Predictions
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?21
1 8
10-5 Making Predictions
I can use probability to predict events.
10-5 Making Predictions
Vocabulary
prediction
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
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 = x4
10
Method 1: Set up an equation.
140 = x
10-5 Making Predictions
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 = 10xDivide each side by 10 to isolate the variable.
140 = x
10 10
4 10
= x 350
10-5 Making Predictions
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
Multiply the probability by the number of attempts.
· 225 = x2
10
Method 1: Set up an equation.
45 = x
10-5 Making Predictions
Think: 2 out of 10 is how many out of 225.
Method 2: Set up a proportion.
The cross products are equal.
Multiply.
2 · 225 = 10 · x
Malia can predict that she will score about 45 goals of 225 attempts.
Check It Out: Example 1 Continued
450 = 10xDivide each side by 10 to isolate the variable.
45 = x
10 10
2 10
= x 225
10-5 Making 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?
Additional Example 2: Using Theoretical Probability to Make Predictions
3 · 50 = 8 · x
P(spinning a 1) = 3 8
Think: 3 out of 8 is how many out of 50.
18.75 = x
3 8
= x 50
The cross products are equal.
Multiply150 = 8x
You can expect to spin a 1 about 19 times.
8 8 Divide each side by 8 to isolate the variable.
10-5 Making Predictions
Round to a whole number if it makes sense in the given situation.
Helpful Hint
10-5 Making 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 2?
Check It Out: Example 2
P(spinning a 2) = 2 8
Think: 2 out of 8 is how many out of 50.
The cross products are equal.
Multiply. Divide each side by 8 to isolate the variable.You can expect to spin a 2 about 13 times.
2 · 50 = 8 · x
12.5 = x
2 8
= x 50
100 = 8x8 8
10-5 Making Predictions
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
10-5 Making Predictions
11 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 5days of their vacation.
Additional Example 3 Continued
10-5 Making Predictions
22 Make a Plan
On average 21 out of the 62 days it is rainy. Afterfinding out the number of rainy days there shouldbe forecast, subtract to find the number of notrainy days.
Additional Example 3 Continued
10-5 Making Predictions
Solve33
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 = 5
21 62
= x 7
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 62
10-5 Making Predictions
Look Back44
They should choose a different location. It islikely to rain more than 2 days (about 2.4 days)during a 7-day period, which will not give theSinghs at least 5 sunny days.
Additional Example 3 Continued
21 rainy days 62 total days
≈ 20 60
or 33%
2.4 rainy days 7 total days
≈ 2 7
or 30%
Since both ratios are about 30%, the answer isreasonable.
10-5 Making Predictions
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
10-5 Making Predictions
11 Understand the Problem
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 4days of their vacation.
Check It Out: Example 3 Continued
10-5 Making Predictions
22 Make a Plan
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.
Check It Out: Example 3 Continued
10-5 Making Predictions
Solve33
Check It Out: Example 3 Continued
Think: 35 out of 60 is how many out of 9.
The cross products are equal.
Multiply.
35 · 9 = 60 · x
9 – 5 = 4
35 60
= x 9
Divide each side by 60 to isolate the variable.
315 = 60x
5.25 = x There will be more than 5 snow days in 9 days.
Subtract the predicted number of snow days from the total vacation days.
60 60
10-5 Making Predictions
Look Back44
They should choose a different location. It islikely to snow more than 5 days during a 9-day period, which will not give the Reids at least 4 days without snow.
Check It Out: Example 3 Continued
35 snow days 60 total days
≈ 35 60
or 58%
5.25 snow days 9 total days
≈ 5 9
or 55%
Since both ratios are about 55%, the answer isreasonable.
10-5 Making Predictions
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
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?
2. If Scott flips two quarters 25 times, how many times can he expect to flip two heads?
6 times
32
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
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
10-5 Making Predictions
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
Lesson Quiz for Student Response Systems