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398 Chapter 9 Probability
STATE
STANDARDS
MA.7.P.7.1
MA.7.P.7.2
S
Experimental Probability
9.3
What is meant by experimental probability?
Play with a partner. This game is based on an
Apache game called “Throw Sticks.”
● Take turns throwing three sticks into the
center of the circle and moving around the
circle according to the chart.
● If your opponent lands on or passes your
playing piece, you must start over.
● The fi rst player to pass his or her starting
point wins.
ACTIVITY: Throwing Sticks
1
1
Each stick has one plain side
and one decorated side.
The game board has
40 stones arranged in
a circle. The stones are
placed in groups of 10.
Players start on
opposite sides
of the circle.
Player 2
Starting Point
Player 1
Starting Point
English
Spanish
Section 9.3 Experimental Probability 399
ACTIVITY: Conducting an Experiment
2
2
Work with a partner. Throw the 3 sticks 32 times. Tally the results using the
outcomes listed below. Organize the results in a bar graph. Use the bar graph
to estimate the probability of each outcome. These are called experimental
probabilities.
a. PPP
b. DPP
c. DDP
d. DDD
DDPDDD DPPDPD PDPPDD PPPPPD
DDP
P
DDD
D
D
P
P
D
D
D
P
DPD
D
P
P
P
D
D
P
D
D
P
P
P
P
PDD
D
D
D P
P
P
D
D
D
PPP
P
PPD
D
P
P
P
D
D
P
Work with a partner. A tree diagram helps you
see different ways that the same outcome
can occur.
a. Find the number of ways that each
outcome can occur.
● Three Ps
● One D and two Ps
● Two Ds and one P
● Three Ds
b. Find the theoretical probability of each outcome.
c. Compare and contrast your experimental and theoretical probabilities.
ACTIVITY: Analyzing the Possibilities
3
3
4. IN YOUR OWN WORDS What is meant by experimental probability?
5. Give a real-life example of experimental probability.
Use what you learned about experimental probability to complete
Exercises 3– 6 on page 402.
English
Spanish
400 Chapter 9 Probability
Lesson
9.3
Key Vocabulary
experimental
probability, p. 400
Experimental Probability
Probability that is based on repeated trials of an experiment is called
experimental probability.
P(event)
number of times the event occurs

total number of trials
EXAMPLE
Standardized Test Practice
1
1
Thirteen out of 20 emails in your inbox are junk emails. What is the
experimental probability that your next email is junk?
○
A 35%
○
B 45%
○
C 55%
○
D
65%
P(event)
number of times the event occurs

total number of trials
P(junk)
13
20
The probability is
13
20
, 0.65, or 65%. The correct answer is
○
D .
You have 13 emails that are junk.
You have a total of 20 emails.
EXAMPLE
Making a Prediction
2
2
It rains 2 out of the last 12 days in March. If this trend continues,
how many rainy days would you expect in April?
Find the experimental probability of a rainy day.
P(event)
number of times the event occurs

total number of trials
P(rain)
2
12
1
6
To make a prediction, multiply the probability of a rainy day by the
number of days in April.
1
6
30 5
You can predict that there will be 5 rainy days in April.
It rains 2 days.
There is a total of 12 days.
Lesson Tutorials
“April showers bring May
fl owers.” Old Proverb, 1557
English
Spanish
Section 9.3 Experimental Probability 401
Exercises 7–18
EXAMPLE
Comparing Experimental and Theoretical Probabilities
3
3
The bar graph shows the results of rolling a number cube
50 times. What is the experimental probability of rolling an
odd number? How does this compare with the theoretical
probability of rolling an odd number?
Find the experimental probability of rolling a 1, 3, or 5.
The bar graph shows 10 ones, 8 threes, and 8 fi ves.
So, an odd number was rolled 10 8 8 26 times in
a total of 50 rolls.
The experimental probability is
13
25
0.52 52%. The theoretical
probability is
1
2
0.5 50%. The experimental and theoretical
probabilities are similar.
3. In Example 3, what is the experimental probability of rolling a
number greater than 1? How does this compare with the
theoretical probability of rolling a number greater than 1?
Exercise 19
Times rolled
Rolling a Number Cube
6
8
10
0
2
4
12
123456
Number rolled
1. In Example 1, what is the experimental probability that your
next email is not junk?
2. At a clothing company, an inspector fi nds
5 defective pairs in a shipment of 200 jeans.
a. What is the experimental probability of
a pair of jeans being defective?
b. About how many would you expect to be
defective in a shipment of 5000 pairs of jeans?
An odd number was rolled 26 times.
There was a total of 50 rolls.
Experimental Probability Theoretical Probability
P(event)
number of times the event occurs

total number of trials
P(event)
number of favorable outcomes

number of possible outcomes
P(odd)
26
50
P(odd)
3
6
13
25
1
2
There are 3 odd numbers.
There is a total of 6 numbers.
English
Spanish
Exercises
9.3
9
+(-6)=3
3
+(-3)=
4
+(-9)=
9
+(-1)=
402 Chapter 9 Probability
1. VOCABULARY Describe how to fi nd the experimental probability of an event.
2. REASONING You fl
ip a coin 10 times and fi nd the experimental probability of
fl ipping tails to be 0.7. Does this seem reasonable? Explain.
You have three sticks. Each stick has one red side and
Outcome Frequency
3 red 4
3 blue 0
2 blue, 1 red 2
2 red, 1 blue 4
one blue side. You throw the sticks 10 times and record
the results. Use the table to fi nd the experimental
probability of the event.
3. Tossing 3 red 4. Tossing 2 blue, 1 red
5. Tossing 2 red, 1 blue 6. Not tossing all red
Use the bar graph to fi nd the experimental probability
of the event.
7. Spinning a 6 8. Spinning an even number
9. Not spinning a 1 10. Spinning a number less than 3
11. Spinning a 1 or a 3 12. Spinning a 7
13. ERROR ANALYSIS Describe and correct the error
in fi nding P(4) using the bar gr
aph.
14. EGGS You check 20 cartons of eggs. Three of the cartons have at least one
cracked egg. What is the experimental probability that a carton of eggs has at
least one cracked egg?
15. BOARD GAME There are 105 lettered
tiles in a boar
d game. You choose the
tiles shown. How many of the 105 tiles
would you expect to be vowels?
16. CARDS You have a package of 20 assorted
thank-y
ou cards. You pick the four cards
shown. How many of the 20 cards would
you expect to have fl owers on them?
P(4)
number of favorable outcomes

number of possible outcomes
1
6
✗
1
1
2
2
Times spun
Spinning a Spinner
6
8
10
0
2
4
12
123456
Number spun
Help with Homework
English
Spanish
Section 9.3 Experimental Probability 403
Solve the equation.
24. 5x 100 25. 75 15x 26. 2x 26 27. 4x 96
28. MULTIPLE CHOICE What is the least common denominator of the fractions
1
16
,
2
19
, and
3
76
?
○
A 16
○
B 76
○
C 304
○
D 1216
17. POPULATION The United States Census Bureau estimates that 6% of Florida’s
residents are children under the age of 5. You randomly select 500 Florida
residents. Predict the number who are children under the age of 5.
18. MUSIC During a 24-hour period, the ratio of pop songs played to rap songs
play
ed on a radio station is 60 : 75.
a. What is the experimental probability that the next song played is rap?
b. Out of the next 90 songs, how many would you expect to be pop?
19. FLIPPING A COIN You fl
ip a coin 20 times. You fl ip heads 12 times.
Compare your experimental probability of fl ipping heads with the
theoretical probability of fl ipping heads.
You roll a pair of number cubes 60 times. You record your results in the bar graph shown.
20. Use the bar graph to fi nd the 21. Use the table to fi nd the theoretical
experimental probability of rolling probability of rolling each sum.
each sum. Which sum is most likely? Which sum is most likely?
22. Compare the probabilities you found in Exercises 20 and 21.
23.
You roll two number cubes. Describe and perform an
experiment to fi nd the probability that the product of the two numbers
rolled is at least 12. How many times did you roll the number cubes?
Times rolled
Rolling Two Number Cubes
6
8
10
0
2
4
12
14
12
Sum rolled
111098765432
3
3
English
Spanish
SKILLS REVIEW HANDBOOK
SECTION 2.5
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