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Name Class Date

video tutor Finding Experimental Probability

You can toss a paper cup to demonstrate experimental probability.

Consider tossing a paper cup. What are the three different ways the cup could land?

Toss a paper cup twenty times. Record your observations in the table.

REFLECT

1a. Which outcome do you think is most likely?

1b. Describe the three outcomes using the words likely and unlikely.

1c. Use the number of times each event occurred to calculate the probability of each event.

1d. What do you think would happen if you performed more trials?

1e. What is the sum of the three probabilities in 1c?

E X P L O R E1

Experimental ProbabilityGoing DeeperEssential question: How do you find the experimental probability of an event?

10-2

Outcome Number of Times

Open-end up

Open-end down

On its side

Outcome Experimental Probability

Open-end up open-end up

_____________ 20

= ____ 20

Open-end down open-end down

________________ 20

= ____ 20

On its side on its side __________ 20

= ____ 20

Chapter 10 401 Lesson 2

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It is sometimes impossible or inconvenient to calculate theoretical probabilities. You can use experimental probability to estimate the probability of an event. The experimental probability of the event is found by comparing the number of times the event occurs to the total number of trials.

Calculating Experimental Probability

Martin has a bag of marbles. He removed one marble, recorded the color and then placed it back in the bag. He repeated this process several times and recorded his results in the table.

A Number of trials =

B Complete the table of experimental probabilities. Write each answer in simplest form.

REFLECT

2. What are two different ways you could find the experimental probability of the event that you do not draw a red marble?

E X AM P L E2Color Frequency

Red 12

Blue 10

Green 15

Yellow 13

Color Experimental Probability

Red frequency of the event

______________________ total number of trials

= ____ = ____

Blue frequency of the event

______________________ total number of trials

= ____ = ____

Green frequency of the event

______________________ total number of trials

= ____ = ____

Yellow frequency of the event

______________________ total number of trials

= ____

Experimental Probability

probability ≈ number of times the event occurs ____________________________ total number of trials

Chapter 10 402 Lesson 2

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Comparing Theoretical and Experimental Probability

A You roll a number cube once. Complete the table of theoretical probabilities for the different outcomes. Remember that theoretical probability is the ratio of the number of ways an event can occur to the total number of equally likely outcomes.

B Using your knowledge of theoretical probability, predict the number of times each number will be rolled out of 30 total rolls.

1: times 3: times 5: times

2: times 4: times 6: times

C Roll a number cube 30 times. Complete the table for the frequency of each number and then find its experimental probability.

D Look at the tables you completed. How do the experimental probabilities compare with the theoretical probabilities?

E Conjecture By performing more trials, you tend to get experimental results that are closer to the theoretical probabilities. Combine your table from C with those of your classmates to make one table for the class. How do the class experimental probabilities compare with the theoretical probabilities?

REFLECT

3. Could the experimental probabilities ever be exactly equal to the theoretical probability? Why or why not?

E X P L O R E3

Number 1 2 3 4 5 6

Theoretical Probability

_____ _____ _____ _____ _____ _____

Number 1 2 3 4 5 6

Frequency

Experimental Probability

Chapter 10 403 Lesson 2

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P R A C T I C E

1. Toss a coin at least 20 times. Record the outcomes in the table.

2. What do you think would happen if you performed more trials?

3. Sonja has a bag of ping pong balls. She removed one ball,recorded the marking and then placed it back in the bag. She repeated this process several times and recorded her results in the table. Find the experimental probability of each marked ping pong ball. Write your answers in simplest form.

Stripes: Polka dots:

Stars: Solid color: Squares:

Use a spinner with six equal sections for 4–6.

4. What is the theoretical probability of landing on a specific section of your spinner?

5. Spin the spinner 30 times. Complete the table.

6. Look at the tables you completed. How do the experimental probabilities compare with the theoretical probabilities?

7. Critical Thinking Patricia finds that the experimental probability of her dog wanting to go outside between 4 !.". and 5 !.". is 7 __ 12 . About what percent of the time does her dog not want to go out between 4 !.". and 5 !.".?

Type Frequency

Stripes 12

Polka dots 13

Stars 18

Solid color 17

Squares 10

Tossing of Coin

Number of Times

Experimental Probability

Heads

Tails

Color or Numbered Section

Frequency

Experimental Probability

Chapter 10 404 Lesson 2

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Find the experimental probability. Write your answer as a fraction, as a decimal, and as percent.

1. Jaclyn is a soccer goalie. If she has 21 out of 25 saves in practice, what is the experimental probability that she will have a save on the next shot on goal? ____________________

2. If Harris hit the bull’s-eye 3 out of 8 times at archery practice, what is the experimental probability that he will hit the bull’s-eye on his next try? ____________________

3. Nathan inspects new pants at a factory. Of the first 56 pairs of pants he inspected 49 were acceptable. What is the experimental probability that the next pair of pants will be acceptable? ____________________

4. Sara has gone to work for 60 days. On 39 of those days she arrived at work before 8:30 A.M. On the rest of the days she arrived after 8:30 A.M. What is the experimental probability that she will arrive at work after 8:30 A.M. the next day she goes to work? ____________________

Solve.

5. After a movie premiere, 99 of the first 130 people surveyed said they liked the movie.

a. What is the experimental probability that the next person surveyed will say he or she liked the movie? _____________

b. What is the experimental probability that the next person surveyed will say he or she did not like the movie? _____________

6. For the past 30 days, Naomi has been recording the number of customers at her restaurant between 10 A.M. and 11 A.M. During that hour, there have been fewer than 20 customers on 25 out of 30 days.

a. What is the experimental probability that there will be fewer than 20 customers on the thirty-first day? _____________

b. What is the experimental probability that there will be 20 or more customers on the thirty-first day? _____________

7. For the past four weeks, Nestor has been recording the daily high temperatures. During that time, the high temperature has been below 45° on 20 out of 28 days. What is the experimental probability that the high temperature will be below 45° on the twenty-ninth day? _____________

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Additional Practice

Name Class Date 10-2

Chapter 10 405 Practice and Problem Solving

52

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Name ________________________________________ Date __________________ Class__________________

Holt McDougal Mathematics

Probability Problem Solving: Experimental Probability

Write the correct answer as a fraction in simplest form. This table shows a breakdown by format of total music sales in the United States in 2004. 1. What is the experimental probability

that any random music purchase in 2004 was a CD?

________________________________________

2. What is the experimental probability that any random music purchase in 2004 was not a Music Video?

________________________________________

3. What is the experimental probability that any random music purchase in 2004 was a digital single?

________________________________________

Total American Music Sales in 2004

Format Total (% of units shipped)

CD 80 Digital Single 15 Music Video 3 Other 2

4. Which combination of sales has an

experimental probability of 1

20?

________________________________________

Choose the letter for the best answer. 5. Ethan hits 4 ringers in 10 attempts

while pitching horseshoes. What

does an experimental probability of 25

describe? A P(horseshoes) B P(missed shots) C P(attempts) D P(ringers)

7. Poonam counts 10 classmates out of 36 people in the library. What is the experimental probability that the next person will be a classmate?

A 536

C 1

36

B 5

18 D

1

10�

6. Jay beats Terry at table tennis 3 out of 5 games. What is the experimental probability that Terry will win their next game?

F 12

H 25

G 35

J 1

8. Macy makes 15 of 20 free throws at

basketball practice. What is the experimental probability that she will miss her next free throw?

F 14

H 23

G 12

J 34�

LESSON

XLESSON

2

CS10_MSM_C2_PSW_P_PRO2.indd 52 4/29/11 5:59:31 AM

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Problem Solving

Chapter 10 406 Practice and Problem Solving