Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
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Warm Up Solve each proportion. 1. Which
represents a greater amount0.04 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
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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
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I can use probability to predict events.
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Vocabulary
prediction
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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.
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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
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Additional Example 1 Continued
Method 2 Set up a proportion.
Think 4 out of 10 is how many out of 350.
The cross products are equal.
4 350 10 x
Multiply.
1400 10x
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.
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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
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Check It Out Example 1 Continued
Method 2 Set up a proportion.
Think 2 out of 10 is how many out of 225.
The cross products are equal.
2 225 10 x
Multiply.
450 10x
Divide each side by 10 to isolate the variable.
10 10
45 x
Malia can predict that she will score about 45
goals of 225 attempts.
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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)
Think 3 out of 8 is how many out of 50.
3 50 8 x
The cross products are equal.
Multiply
150 8x
Divide each side by 8 to isolate the variable.
18.75 x
You can expect to spin a 1 about 19 times.
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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)
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
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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?
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Additional Example 3 Continued
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.
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Additional Example 3 Continued
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.
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Additional Example 3 Continued
Think 21 out of 62 is how many out of 7.
The cross products are equal.
21 7 62 x
Multiply.
147 62x
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
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Additional Example 3 Continued
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.
Since both ratios are about 30, the answer
is reasonable.
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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?
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Check It Out Example 3 Continued
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.
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Check It Out Example 3 Continued
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.
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Check It Out Example 3 Continued
Think 35 out of 60 is how many out of 9.
The cross products are equal.
35 9 60 x
Multiply.
315 60x
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
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Check It Out Example 3 Continued
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.
Since both ratios are about 55, the answer
is reasonable.
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Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
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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
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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.
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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
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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