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Introduction to Probability
BEFORE
Now
WHY?
You wrote ratios.
You’ll find probabilities.
So you can find the probability of
making a free throw, as in Ex. 16.
In the Real World
Cat Tricks A cat that knows the shake
command offers either of its front paws
to shake. The table shows the number
of times the cat offered each of its paws
when asked to shake. What is the likelihood
that the cat will offer its right paw when
asked to shake? You’ll find out in Example 2.
Word Watch
outcomes, p. 634
event, p. 634
favorable outcomes, p. 634
probability, p. 634
theoretical probability,
p. 635
experimental probability,
p. 635
Paw Offered to Shake
Left paw
38
Right paw
12
When you perform an experiment, the possible results are called
outcomes . An event is a collection of outcomes. Once you specify an
event, the outcomes for that event are called favorable outcomes .
The probability of an event is a measure of the likelihood that the event
will occur. Use the formula below to find the probability P of an event
when all of the outcomes are equally likely.
Number of favorable outcomes
Total number of outcomes
P(event) EXAMPLE
with
Solving
You can write probabilities
as fractions, decimals, or
percents.
1
Finding a Probability
Find the probability of randomly choosing
a blue marble from the marbles shown
at the right.
3
10
P(blue) There are 3 blue marbles.
There are 10 marbles in all.
ANSWER The probability of choosing a blue marble
3
10
is , 0.3, or 30%.
Probabilities can range from 0 to 1. The closer the probability of an
event is to 1, the more likely the event will occur.
P0
Impossible
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Chapter 13
Probability
P 0.25
Unlikely
P 0.5
Likely to occur
half the time
P 0.75
Likely
P1
Certain
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Your turn now
Find the probability of the event.
1. From the marbles in Example 1, you randomly choose
a green marble.
2. You get tails when you flip a coin.
3. You get a 5 when you roll a number cube.
with
Solving
Experimental probabilities
can be based on scientific
experiments, surveys,
historical data, or simple
activities.
Types of Probability The probability found in Example 1 is a
theoretical probability because it is based on knowing all of the
equally likely outcomes. Probability that is based on repeated trials of
an experiment is called an experimental probability . Each trial in
which the event occurs is a success.
Use the formula below to find the experimental probability of an event.
Number of successes
Number of trials
Experimental probability of an event EXAMPLE
2
Finding an Experimental Probability
To find the probability that the cat will offer its right paw when asked to
shake, use the information in the table on page 634.
1 Determine the number of successes and the number of trials.
Because a success is offering a right paw, there are 12 successes.
There are 38 12 50 trials.
2 Find the probability.
12
50
6
25
There are 12 successes.
There are 50 trials.
P(right paw) Simplify.
ANSWER The probability that the cat will offer its right paw when asked
6
25
to shake is , 0.24, or 24%.
Your turn now
Solve the following problems.
4. In Example 2, what is the probability that the cat will offer its left
paw when asked to shake?
5. Of the 20 voters polled after an election for class president, 14 of the
voters voted for Sean. What is the probability that a randomly
chosen voter voted for Sean?
Lesson 13.1
Introduction to Probability
635
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Exercises
eWorkbook Plus
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More Practice, p. 717
Getting Ready to Practice
1. Vocabulary Copy and complete: The _?_ of an event is a measure of
the likelihood that the event will occur.
Suppose you spin the spinner below, which is divided into equal
parts. Match the event with the letter on the number line that
indicates the probability of the event.
A
0
B
0.25
C
D
0.5
0.75
2
7
1
5
10
6
12
2. Pointer lands on green.
3. Pointer lands on 7.
4. Pointer lands on an even number.
4
8
5. Pointer lands on a prime number.
Practice and Problem Solving
with
Homework
Each letter in MISSISSIPPI is written on a separate piece of paper
and put into a bag. You randomly choose a piece of paper from the
bag. Find the probability of the event. Write the probability as a
fraction.
Example Exercises
1
6–14, 21
2
15–18, 21
Online Resources
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• More Examples
• eTutorial Plus
6. You choose an M.
7. You choose an I.
8. You choose an S.
9. You choose a P.
You randomly choose a marble from the marbles below. Find the
probability of choosing a marble of the given color. Write the
probability as a fraction, a decimal, and a percent.
10. Blue
11. Red
12. Green
13. Yellow
14. Cereal Each box of your favorite cereal contains one of two action
figures from a movie. A supermarket has 50 boxes of the cereal. In 30
of the boxes there is an action figure of the hero, and in 20 of the boxes
there is an action figure of the villain. What is the probability that you
randomly choose a box of cereal that has the action figure of the hero?
636
Chapter 13
Probability
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15. Tongue Rolling You asked 80 students at your school whether they
Science
can roll their tongues. Of the students surveyed, 64 said yes. Find the
probability that a randomly selected student can roll his or her tongue.
Write the probability as a fraction, a decimal, and a percent.
Basketball The table below shows the shots attempted and made
by Kobe Bryant in basketball games during a season. Find the
probability that Bryant makes the given shot. Write the probability
as a decimal rounded to the nearest hundredth.
16. Free throw
Free throw
Two point
Three point
17. Two point
Attempted
589
1597
132
18. Three point
Made
488
749
33
19. Critical Thinking Suppose Abby tosses a baseball hat. Abby reasons
that because the hat will land in one of two positions (right side up, or
upside down), the probability of the hat landing upside down is 50%.
What is wrong with Abby’s reasoning?
■
Tongue Rolling
The ability to roll your
tongue into a U-shape is a
genetic trait inherited from
your parents. The results
of a survey state that 78%
of people can roll their
tongues. If 500 people
were surveyed, then how
many of the people
surveyed can roll their
tongues?
20. Writing Describe the difference between theoretical and experimental
probability.
21. Collect Data What is the theoretical probability of getting tails when
flipping a coin? Flip a coin 20 times and record the outcomes. Find the
experimental probability and compare it with the theoretical
probability.
Finding Odds In Exercises 22–24, you are playing a game which
uses the spinner in the following example. The spinner is divided
into equal parts. Find the odds in favor and the odds against the
event.
EXAMPLE
Finding Odds
The odds in favor and the odds against the pointer landing on orange
are shown below.
Favorable outcomes
Unfavorable outcomes
3
7
Odds in favor The odds in favor of landing on orange are 3 to 7.
Unfavorable outcomes
Favorable outcomes
7
3
Odds against The odds against landing on orange are 7 to 3.
22. Lands on blue
23. Lands on green
Lesson 13.1
24. Lands on yellow
Introduction to Probability
637
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Automobiles In Exercises 25 and 26, use the circle graph, which
shows the popularity of colors for new automobiles among
Americans.
25. Of the 200 new automobiles
in a parking lot, how many
would you expect to be blue?
26. If a parking lot has 30 new
automobiles that are red, how
many of the automobiles in
the lot would you expect to be
new?
Automobile Color Choices
Red 12%
White 17%
Black 11%
Silver 21%
Blue 10%
Other 21%
Green 8%
27. Marbles A bag contains red and blue marbles. The probability of
randomly choosing a red marble is 25%, and the probability of
randomly choosing a blue marble is 75%. Determine the number of red
marbles and blue marbles in the bag if there is a total of 16 marbles in
the bag.
28. Challenge Find the theoretical probability of flipping a coin three
times and getting tails each time.
Mixed Review
29. Sketch a quadrilateral that has four right angles and four congruent
sides. Then classify the quadrilateral. (Lesson 10.4)
30. Find the height of a cylinder with a radius of 4 feet and a volume of
502.4 cubic feet. Use 3.14 for π. (Lesson 12.6)
Basic Skills Find the product.
1
31. 3 3
2
1
4
32. 1 3
5
2
1
33. 2 2 7
4
1
3
34. 4 6 6
5
Test-Taking Practice
35. Multiple Choice Tanya decides to listen to a CD with 12 songs, 3 of
INTERNET
which are her favorite songs. If Tanya listens to the CD in random play,
what is the probability that the first song played is one of her favorites?
State Test Practice
CLASSZONE.COM
1
4
A. 1
3
B. 1
2
C. 3
4
D. 36. Short Response At a blood drive held at a school, 2 students out of the
40 students who gave blood have type AB blood. Find the probability
that a randomly selected student has type AB blood. Write the
probability as a fraction, a decimal, and a percent.
638
Chapter 13
Probability