10-5 Making Predictions
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
10-5 Making Predictions
Warm Up
Solve each proportion.
1. Which represents a greater amount–0.04 or 3.9
percent?
0.04
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
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 1. If she was successful on 3 tries, how
8
many times did she miss?
21
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
Additional Example 1: Using Experimental
Probability to Make Predictions
Lawrence finds the experimental probability of
his reaching first base is 40%. Out of 350 atbats, how many times can he expect to reach
first base?
Method 1: Set up an equation.
4
· 350 = x
10
140 = x
Multiply the probability by the number
of at bats.
10-5 Making Predictions
Additional Example 1 Continued
Method 2: Set up a proportion.
x
4
=
350
10
4 · 350 = 10 · x
1400 = 10x
10
10
140 = x
Think: 4 out of 10 is how many out
of 350.
The cross products are equal.
Multiply.
Divide each side by 10 to isolate the
variable.
Lawrence can predict that he will reach first base about
140 of 350 times.
10-5 Making Predictions
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
· 225 = x
10
45 = x
Multiply the probability by the number
of attempts.
10-5 Making Predictions
Check It Out: Example 1 Continued
Method 2: Set up a proportion.
x
2
=
225
10
2 · 225 = 10 · x
450 = 10x
10
10
45 = x
Think: 2 out of 10 is how many out
of 225.
The cross products are equal.
Multiply.
Divide each side by 10 to isolate the
variable.
Malia can predict that she will score about 45 goals of
225 attempts.
10-5 Making Predictions
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?
P(spinning a 1) = 3
8
Think: 3 out of 8 is how many
3
x
=
out of 50.
8
50
3 · 50 = 8 · x
The cross products are equal.
150 = 8x
8
8
Multiply
Divide each side by 8 to isolate
the variable.
You can expect to spin a 1
about 19 times.
18.75 = x
10-5 Making Predictions
Helpful Hint
Round to a whole number if it makes
sense in the given situation.
10-5 Making Predictions
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
P(spinning a 2) = 8
2
x
Think: 2 out of 8 is how many
=
8
50
out of 50.
2 · 50 = 8 · x The cross products are equal.
100 = 8x
8
8
12.5 = x
Multiply. Divide each side by
8 to isolate the variable.
You can expect to spin a 2
about 13 times.
10-5 Making Predictions
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?
10-5 Making Predictions
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.
•
10-5 Making Predictions
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.
10-5 Making Predictions
Additional Example 3 Continued
3
Solve
x
21
=
7
62
Think: 21 out of 62 is how many out of 7.
21 · 7 = 62 · x The cross products are equal.
147 = 62x
62
62
2.37 ≈ x
7–2=5
Multiply.
Divide each side by 62 to isolate the
variable.
There will be more than 2 rainy days
in 7 days.
Subtract the predicted number of rainy
days from the total vacation days.
10-5 Making Predictions
Additional Example 3 Continued
4
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 ≈ 20 or 33%
62 total days
60
2.4 rainy days ≈ 2 or 30%
7 total days
7
Since both ratios are about 30%, the answer is
reasonable.
10-5 Making Predictions
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?
10-5 Making Predictions
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.
•
10-5 Making Predictions
Check It Out: Example 3 Continued
2
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.
10-5 Making Predictions
Check It Out: Example 3 Continued
3
Solve
x
35
=
9
60
Think: 35 out of 60 is how many out of 9.
35 · 9 = 60 · x The cross products are equal.
315 = 60x
60
60
5.25 = x
9–5=4
Multiply.
Divide each side by 60 to isolate the
variable.
There will be more than 5 snow days
in 9 days.
Subtract the predicted number of snow
days from the total vacation days.
10-5 Making Predictions
Check It Out: Example 3 Continued
4
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 ≈ 35 or 58%
60 total days
60
5.25 snow days ≈ 5 or 55%
9 total days
9
Since both ratios are about 55%, the answer is
reasonable.
10-5 Making Predictions
Lesson Quizzes
Standard Lesson Quiz
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?
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
10-5 Making Predictions
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