7.SP.8C [552085]
Student
Class
Date
1. Jack plays basketball for his school team. When Jack attempts free
throws, on average he makes 75% of his attempts and misses 25% of his
attempts. Suppose Jack attempts 12 free throws. To find the probability
that Jack will make at least 9 of the 12 attempts, a simulation modeling
his free throws using random numbers from 1 to 4 is created. Numbers 1,
2, and 3 represent attempts Jack makes and number 4 represents
attempts Jack misses. The results of the simulation are shown below.
Part A. Complete the last column of the simulation to find the baskets he
makes.
Part B. Calculate the experimental probability that Jack scores at least
75% of his baskets.
Part C. Charlie also plays basketball for the school team. When Charlie
shoots free throws, he usually makes 60% of the baskets he shoots.
Design a simulation using random numbers to estimate the probability
that Charlie will make 9 of the next 15 baskets he shoots. Be sure to
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explain what numbers you would use and how you would calculate the
experimental probability.
Use words, numbers, and/or pictures to show your work.
2. Sarah rolled a fair number cube 20 times. The results are shown in the table.
Based on the data, what is the probability of rolling a 3 or a 5?
A.
B.
C.
D.
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3. Daniel performed an experiment. He placed different-colored balls in a
bag. He pulled 1 ball out of the bag randomly, recorded the color, and put
the ball back in the bag. He repeated this process a total of 100 times.
The results of the experiment are shown in the table below.
Based on the results of the experiment, what is the probability of drawing
a red ball 2 times in a row?
A.
B.
C.
D.
4. Probability Simulation
Erica looks over a quiz her older brother took in his Advanced Japanese
class. Erica does not read Japanese, the language in which the quiz is
written, but decides to answer the quiz questions for fun. The quiz has five
multiple-choice questions, each with four answer choices.
Erica decides to guess the answer to each question randomly.
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Part A
Decide what outcome will represent a correct answer. For example, if you
are using the randInt() function on a graphing calculator, you could set
the minimum as 1 and the maximum as 4 and let 4 represent a correct
answer.
Part B
In 5 trials (representing the five questions of the quiz), count the number
of 4s (representing the correct answer). Conduct 1 run.
If 4 represents a correct answer, how many questions did Erica get
correct? If 60% represents a passing grade, did Erica pass her test?
Do you think one run of this simulation is enough to predict whether Erica
will pass her test? How many runs do you think will be necessary?
Part C
Conduct 99 more runs of this simulation. This will represent Erica taking
the quiz 100 times, each time answering the five questions randomly.
Part D
On your own paper, create a histogram to display your results,
representing the frequencies that Erica scored 0 questions correct, 1
question correct, 2 questions correct, 3 questions correct, 4 questions
correct, and 5 questions correct.
Part E
On your own paper, summarize your findings. Report the experimental
probability that Erica will pass the Japanese quiz, and use this to decide
whether choosing a random answer is a good way to take the quiz.
Part F
Design and run your own simulation for using probability to take a 5question quiz where each question has either true or false as an answer.
On your own paper, summarize your findings.
5. Suri wants to estimate the probability of getting 7 tails when a fair coin is
tossed 9 times. She uses random digits to represent one outcome for this
experiment. Each digit comes from the set of numbers 0 through 9 and is
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chosen randomly by a computer. If the digit is 0, 1, 2, 3 or 4, the coin is
considered to have landed on heads. If the digit is any other number, the
coin is considered to have landed on tails. How many random digits will
Suri use to represent one outcome for this experiment?
A. 1
B. 2
C. 7
D. 9
6. Michael read on the Internet that 10% of all people are left-handed. He
designed a simulation with random digits. Michael used the digits 0
through 8 to represent people who are right-handed. He used the digit 9
to represent people who are left-handed. Each list of digits represents a
group of ten people walking into Michael’s school. Which list shows three
of the people in a row being left-handed?
A.
1193718293
B.
0017202999
C.
0119129958
D.
3581372951
7. A student has this problem: “A baseball player makes a hit 30% of the
time. How many times will he hit the ball in the next 10 attempts?” The
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student decided to simulate this problem using a spinner. Which
statement describes how the student should design and use the spinner?
A.
Divide the spinner into 10 equal sections and spin the spinner 10
times.
B.
Divide the spinner into 30 equal sections and spin the spinner 10
times.
C.
Divide the spinner into two sections measuring
spin the spinner 10 times.
and
Divide the spinner into two sections measuring
the spinner 10 times.
and
and
D.
and spin
Random Arrangements
8.
Tess is exploring different assigned seating arrangements and wondering
which situation gives the greatest probability that she will be able to sit
with her friend Emerson.
Part A. Consider a round table that seats 10 people. If seats are assigned
randomly to 10 people, including Tess and Emerson, what is the
probability that Tess will sit next to her friend? Assume that Tess can sit in
any of the 10 seats. Explain your answer.
Part B. Find an online random number generator like the one on
stattrek.com. After getting familiar with how it works, design an
experiment to simulate the problem in Part A. Describe how your
experiment would work.
Part C. Run your simulation at least 40 times. Create and fill in a table to
record how many times it gives the desired result, that is, that Tess and
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Emerson sit next to each other. Every 10 simulations, calculate the
cumulative probability of the simulation. Express the probability as a
decimal, and compare it to your theoretical probability from Part A. If
other students are doing the experiment as well, combine the results of all
the trials and give the experimental probability.
Part D. Now consider a classroom with 6 groups of 4 desks each. If 24
students are assigned to the desks randomly, what is the probability that
Tess and Emerson will be in the same group? Explain your answer.
Part E. Design an experiment to simulate the problem in Part D using a
random number generator. Describe how your experiment would work.
Part F. Run your simulation at least 40 times. Create and fill in a table to
record how many times it gives the desired result; that is, that Tess and
Emerson sit in the same group of desks. Every 10 simulations, calculate
the cumulative probability of the simulation. Express the probability as a
decimal, and compare it to your theoretical probability from Part D. If
other students are doing the experiment as well, combine the results of all
the trials and give the experimental probability.
Use words, numbers, and/or pictures to show your work.
9. A company has found that 60% of the purchases for its goods come from
other countries. It wants to conduct a simulation of the purchases using
random numbers. Which simulation will provide the company with the
most accurate data?
A. choose a random number from 0 to 9, with 1 through 6 representing a
purchase from another country
B. choose a random number from 1 to 99, with 1 through 60
representing a purchase from another country
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C. choose a random number from 1 to 9, with 1 through 6 representing a
purchase from another country
D. choose a random number from 0 to 100, with 1 through 60
representing a purchase from another country
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