Download Holt Ch11 Lesson 2

11-2 Experimental Probability
Warm Up
Problem of the Day
Lesson Presentation
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11-2 Experimental Probability
Warm Up
Write impossible, unlikely, equally likely,
likely, or certain to describe each event.
1. A particular person’s birthday falls on the first of
a month. unlikely
2. You roll an odd number on a fair number cube.
equally likely
3. There is a 0.14 probability of picking the winning
ticket. Write this as a fraction and as a percent.
7 , 14%
__
50
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11-2 Experimental Probability
Problem of the Day
Max picks a letter out of this problem at
random. What is the probability that the
letter is in the first half of the alphabet?
57
___
101
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11-2 Experimental Probability
Learn to find the experimental probability
of an event.
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11-2 Experimental
Insert LessonProbability
Title Here
Vocabulary
experiment
outcome
sample space
experimental probability
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11-2 Experimental Probability
An experiment is an activity involving chance
that can have different results. Flipping a coin and
rolling a number cube are examples of
experiments.
The different results that can occur are called
outcomes of the experiment. If you are flipping
a coin, heads is one possible outcome.
The sample space of an experiment is the set of
all possible outcomes. You can use {} to show
sample spaces. When a coin is being flipped,
{heads, tails} is the sample space.
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11-2 Experimental Probability
Additional Example 1A: Identifying Outcomes
and Sample Spaces
For each experiment, identify the outcome
shown and the sample space.
A. Spinning two spinners
outcome shown: B1
sample space: {A1, A2, B1, B2}
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11-2 Experimental Probability
Additional Example 1B: Identifying Outcomes
and Sample Spaces
For each experiment, identify the outcome
shown and the sample space.
B. Spinning a spinner
outcome shown: green
sample space: {red, purple, green}
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11-2 Experimental Probability
Try This: Example 1A
For each experiment, identify the outcome
shown and the sample space.
A. Spinning two spinners
C
D
3
4
outcome shown: C3
sample space: {C3, C4, D3, D4}
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11-2 Experimental Probability
Try This: Example 1B
For each experiment, identify the outcome
shown and the sample space.
B. Spinning a spinner
outcome shown: blue
sample space: {blue, orange, green}
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11-2 Experimental Probability
Performing an experiment is one way to estimate
the probability of an event. If an experiment is
repeated many times, the experimental
probability of an event is the ratio of the
number of times the event occurs to the total
number of times the experiment is performed.
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11-2 Experimental Probability
Writing Math
The probability of an event can be written
as P(event). P(blue) means “the
probability that blue will be the outcome.”
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11-2 Experimental Probability
Additional Example 2: Finding Experimental
Probability
For one month, Mr. Crowe recorded the time at
which his train arrived. He organized his results
in a frequency table.
Time
Frequency
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6:49-6:52 6:53-6:56 6:57-7:00
7
8
5
11-2 Experimental Probability
Additional Example 2A Continued
A. Find the experimental probability that the
train will arrive before 6:57.
Before 6:57 includes 6:49-6:52 and 6:53-6:56.
of times the event occurs
___________________________
P(before 6:57)  number
total number of trials
7+8
_____
=
20
3
15
__
___
=
=
4
20
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11-2 Experimental Probability
Additional Example 2B: Finding Experimental
Probability
B. Find the experimental probability that
the train will arrive between 6:53 and 6:56.
number
of times the event occurs
___________________________
P(between 6:53 and 6:56) 
total number of trials
2
8
__
___
=
=
5
20
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11-2 Experimental Probability
Try This: Example 2
For one month, Ms. Simons recorded the time at
which her bus arrived. She organized her results
in a frequency table.
Time
Frequency
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4:31-4:40 4:41-4:50 4:51-5:00
4
8
12
11-2 Experimental Probability
Try This: Example 2A
A. Find the experimental probability that the
bus will arrive before 4:51.
Before 4:51 includes 4:31-4:40 and 4:41-4:50.
of times the event occurs
___________________________
P(before 4:51)  number
total number of trials
4+8
_____
=
24
1
12
__
___
=
=
2
24
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11-2 Experimental Probability
Try This: Example 2B
B. Find the experimental probability that
the bus will arrive between 4:41 and 4:50.
number
of times the event occurs
___________________________
P(between 4:41 and 4:50) 
total number of trials
1
8
__
___
=
=
3
24
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11-2 Experimental Probability
Additional Example 3: Comparing
Experimental Probabilities
Erika tossed a cylinder 30 times and recorded
whether it landed on one of its bases or on its
side. Based on Erika’s experiment, which way
is the cylinder more likely to land?
Outcome
Frequency
On a base
On its side
llll llll
llll llll llll llll l
Find the experimental probability of each outcome.
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11-2 Experimental Probability
Additional Example 3 Continued
number
of times the event occurs ___
9
___________________________
P(base) 
=
total number of trials
30
number
of times the event occurs ___
21
___________________________
P(side) 
=
total number of trials
30
9
21
___
___
<
30
30
Compare the probabilities.
It is more likely that the cylinder will land on its
side.
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11-2 Experimental Probability
Try This: Example 3
Chad tossed a cylinder 25 times and recorded
whether it landed on one of its bases or on its
side. Based on Chads’s experiment, which
way is the cylinder more likely to land?
Outcome
Frequency
On a base
On its side
llll
llll llll llll llll
Find the experimental probability of each outcome.
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11-2 Experimental Probability
Try This: Example 3 Continued
number
of times the event occurs ___
5
___________________________
P(base) 
=
total number of trials
25
number
of times the event occurs ___
20
___________________________
P(side) 
=
total number of trials
25
5
20
___
___
<
25
25
Compare the probabilities.
It is more likely that the cylinder will land on its
side.
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11-2 Experimental
Insert LessonProbability
Title Here
Lesson Quiz: Part 1
1. The spinner below was spun. Identify the
outcome shown and the sample space.
outcome: green; sample
space: {red, blue, green,
purple, yellow}
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11-2 Experimental
Insert LessonProbability
Title Here
Lesson Quiz: Part 2
Sandra spun the spinner above several times
and recorded the results in the table.
2. Find the experimental probability that the
2
spinner will land on blue. __
9
3. Find the experimental probability that the
4
spinner will land on red. __
9
4. Based on the experiment, on which color will
the spinner most likely land?
red
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