1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. 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

3. 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

4. Learn to use probability to predict events.

5. Vocabulary
prediction

6. 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.

7. 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

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

9. · 225 = x 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

10. Check It Out: Example 1 Continued
Method 2: Set up a proportion.
2 10 = x
Think: 2 out of 10 is how many out of 225.
2 · 225 = 10 · x
The cross products are equal.
450 = 10x
Multiply.
Divide each side by 10 to isolate the variable.
45 = x
Malia can predict that she will score about 45 goals of 225 attempts.

11. 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) =
3 8 =
x 50
Think: 3 out of 8 is how many out of 50.
3 · 50 = 8 · x
The cross products are equal.
150 = 8x
Multiply
Divide each side by 8 to isolate the variable.
18.75 = x
You can expect to spin a 1 about 19 times.

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

13. 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) =
2 8 =
x 50
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.
You can expect to spin a 2 about 13 times.
12.5 = x

14. 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?

15. Understand the Problem
Additional Example 3 Continued 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.

16. Additional Example 3 Continued2
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.

17. Additional Example 3 Continued
Solve 3
21 62 = x
Think: 21 out of 62 is how many out of 7.
21 · 7 = 62 · x
The cross products are equal.
147 = 62x
Multiply.
Divide each side by 62 to isolate the variable.
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

18. Additional Example 3 Continued4
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.
21 rainy days 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 is
reasonable.

19. 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?

20. Understand the Problem
Check It Out: Example 3 Continued 1
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 4
days of their vacation.

21. Check It Out: Example 3 Continued2
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.

22. Check It Out: Example 3 Continued
Solve 3
35 60 = x
Think: 35 out of 60 is how many out of 9.
35 · 9 = 60 · x
The cross products are equal.
315 = 60x
Multiply.
Divide each side by 60 to isolate the variable.
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

23. Check It Out: Example 3 Continued4
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.
35 snow days 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 is
reasonable.

24. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 24 24 24

25. 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

26. 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.

27. 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 27 27 27 27

28. 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 28 28 28 28