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7th Grade Review 16&17
Write the best answer.
1. An experiment consists of spinning a spinner 60 times.
a.
List the sample space for the experiment._____________________________________________
b.
How many times do you expect the spinner to land on each number?_____________
c.
Determine the probability of landing on each number._____________
d.
Results from spinning the spinner 60 times are shown in the table. Calculate the experimental
probabilities to complete the table.
Number
Tally
Total
1
18
2
20
3
22
Probability
e.
Compare the experimental probabilities to the theoretical probabilities you calculated in part (c). Are they
the same or different? ____________Explain why.____________________________________
________ ______ ______
________ ______ __
__________________________________________________________________________
2. Suppose the probability is
% that a seed will sprout. Design a simulation to determine how many seeds will
sprout if a gardener plants 5 seeds in a pot.
a.
What are the possible outcomes?___________________________________________
For each experiment, list all the possible outcomes, the sample space, and one possible event. Then, calculate the
probability of the event.
3. rolling a number cube
Possible outcomes_________________________________________
Sample space_____________________________________________
One possible event_____________
Probability of the event___________________
4.
Possible outcomes_________________________________________
Sample space_____________________________________________
One possible event_____________
Probability of the event___________________
5. A restaurant chain includes one of five toy action figures with each child’s meal. The figures come in five
colors: pink, blue, green, purple, and orange. Amanda wants to know what the likelihood is that a child’s meal
will come with a purple action figure.
a.
The experiment was simulated 30 times and the results are shown in the table. Graph the results using a
dot plot and explain what the graph shows.
Trial Number
Result
Trial Number
Result
1
1
16
4
2
3
4
5
6
7
8
9
10
11
12
13
14
15
4
1
3
1
1
5
4
3
2
4
5
4
3
5
17
18
19
20
21
22
23
24
25
26
27
28
29
30
1
3
4
3
5
4
3
2
1
2
3
5
5
2
Multiple Choice
____
6. Sarah rolled a number cube 30 times and recorded the results. She found that she rolled an even number 16 times.
What does
a.
b.
c.
d.
____
represent?
theoretical probability
sample space
experiment
experimental probability
7. When using a graphing calculator to generate random numbers, what will you get if you enter randInt(1, 12, 3)?
a.
b.
c.
d.
3 random integers between 1 and 12
12 random integers between 1 and 3
1 random integer between 1 and 12
random integers between 1 and 123
____
8. Emily is a very good student. She is more likely to attend class than to miss class. Which could be the probability
that she misses class tomorrow?
a.
b.
c.
d.
____
0.4
0.1
0.7
1.2
9. Which would not be an appropriate way to generate 10 random integers to use in one trial of a probability
simulation?
a.
b.
c.
d.
Make a list of the first 10 integers that come to your mind.
Use a random number table.
Use a computer spreadsheet.
Use a random number generator on a graphing calculator.
____ 10. Reba selects 1 card from each of these 3 piles. What is the probability that she selects 3 even numbers?
a.
b.
c.
d.
____ 11. There are 4 boys and 2 girls in the Science Club. The members draw straws to determine which two members will
give the demonstration at the science fair. Which simulation could be used to determine the probability that at
least one of the demonstrators will be a girl?
a.
b.
c.
d.
toss a coin two times
spin a spinner with 4 equal sections two times
roll a six-sided number cube two times
pick a card from 10 cards two times
____ 12. Rico spins the spinner twice and determines the product of the spins. What is the probability
that Rico will get a product of 20?
a.
b.
c.
d.
13. In the game of bridge, a player’s hand contains 13 cards. Kayla was dealt a hand containing 4 spades, 2 hearts, 3
diamonds, and 4 clubs.
a.
Complete the probability model for picking a card at random from Kayla’s hand.
Outcome
Probability
Spade
Heart
Diamond
Club
b.
Determine whether this probability model is a uniform or non-uniform probability model. ____________
Explain your reasoning._________________________________________________________________
c.
What is the probability that the card that is picked will be a red card? (Hearts and diamonds are the red
cards.)______________________
14. An experiment consists of spinning the spinner one time.
a.
How many possible outcomes are
there?_______________________
b.
List the sample space for the
experiment.___________________________________
c.
Determine the probability of the spinner landing on a number _____________or a letter___________.
List the outcomes in this event. ________________________
Then, calculate the probability.______________
d.
Determine the probability of the spinner landing on a consonant________ or an odd number_________.
List the outcomes in this event.______________________________
Then, calculate the probability._______
15. An experiment consists of tossing a coin 50 times.
a.
List the sample space for the experiment._______________________
b.
How many times do you expect the coin to land on each side?______________________________
c.
Determine the probability of heads and the probability of tails.___________________________
d.
Results from tossing the coin 50 times are shown in the table. Calculate the experimental probabilities to
complete the table.
Side
Heads
Tails
Tally
Total
23
27
Probability
e.
Compare the experimental probabilities to the theoretical probabilities you calculated in part (c). Are they
the same or different? ___________Explain why._____________________________________________
___________________________________________________________________________________________
16. There are 100 decks of standard playing cards. Each deck contains 52 cards, and each card is one of four suits—
clubs, diamonds, hearts, or spades. Suppose you wanted to determine the experimental probability of choosing a
club from the 100 decks of playing cards.
a.
What are the possible outcomes?___________________________________________
b.
What two numbers will you use in this function to produce the random integers to simulate a trial for
picking a club?___________________ Explain.__________________________________________
c.
Would it be better to simulate 25 trials or 100 trials? ___________Explain.____________________
_________________________________________________________________________________
17. Jonathan took a 3-question true-false quiz and guessed the answer to each question.
a.
Complete the tree diagram. C represents a correct answer and W represents a wrong answer.
b.
List all of the possible outcomes._______________________________________________
c.
In order to figure out how well he should expect to do on the quiz, Jonathan decided to construct a
probability model for answering 0, 1, 2, and 3 questions correctly. Complete the probability model.
Number of Questions
Answered Correctly
Probability
0
1
2
3
d.
What is the probability of guessing at least 2 answers correctly?_________________
e.
What is the complementary event for “guessing all three questions correctly”?__________________
18. You spin each spinner once. On the spinners, R represents red, B represents
blue, G represents green, Y represents yellow, and P represents purple.
a.
Create an organized list of all the possible
outcomes.__________________________________
b.
What is the probability that both spinners will land on the same
color?___________________
c.
What is the probability that the first spinner will land on Red and the second spinner will land on
Purple?________________
d.
What is the probability that the first spinner will land on Red or the second spinner will land on
Purple?_______________
7th Grade Review 16&17
Answer Section
1. ANS:
a.
{1, 2, 3}
b.
1: 20 times
2: 20 times
3: 20 times
c.
d.
Number
e.
Tally
Total
1
18
2
20
3
22
Probability
The probabilities are different. Experimental probability is determined from doing an experiment. You
may not always get the same results as what is expected from the theoretical probability when you do an
experiment.
PTS: 1
REF: 16.2
NAT: 7.SP.5 | 7.SP.6 | 7.SP.7.a | 7.SP.7.b
TOP: Post Test
KEY: experimental probability
2. ANS:
a.
0, 1, 2, 3, 4, 5
PTS: 1
REF: 16.5
TOP: Post Test
KEY: spreadsheet
3. ANS:
outcomes: 1, 2, 3, 4, 5, 6
NAT: 7.SP.6 | 7.SP.7.a | 7.SP.7.b
sample space: {1, 2, 3, 4, 5, 6}
event: (Sample answer) rolling a number greater than 3
P(number greater than 3)
PTS: 1
REF: 16.1
NAT: 7.SP.5
TOP: Mid Ch Test
KEY: outcome | experiment | sample space | event | simple event | probability | equally likely
4. ANS:
No.
cannot be the probability of an event because a probability can never be less than 0.
PTS: 1
REF: 16.1
NAT: 7.SP.5
TOP: Mid Ch Test
KEY: outcome | experiment | sample space | event | simple event | probability | equally likely
5. ANS:
d.
Sample answer: The graph shows that the likelihood of getting any particular action figure is about equal. The
likelihood, or probability, of getting a purple action figure is about
6.
7.
8.
9.
10.
11.
12.
13.
PTS:
TOP:
ANS:
TOP:
KEY:
ANS:
TOP:
ANS:
TOP:
KEY:
ANS:
TOP:
ANS:
NAT:
KEY:
ANS:
TOP:
ANS:
TOP:
ANS:
a.
1
REF: 16.5
NAT: 7.SP.6 | 7.SP.7.a | 7.SP.7.b
End Ch Test KEY: spreadsheet
D
PTS: 1
REF: 16.1
NAT: 7.SP.5
Standardized Test
outcome | experiment | sample space | event | simple event | probability | equally likely
A
PTS: 1
REF: 16.5
NAT: 7.SP.6 | 7.SP.7.a | 7.SP.7.b
Standardized Test
KEY: spreadsheet
B
PTS: 1
REF: 17.1
NAT: 7.SP.7.a | 7.SP.7.b
Standardized Test
probability model | uniform probability model | non-uniform probability model
A
PTS: 1
REF: 17.4
NAT: 7.SP.8.c
Standardized Test
A
PTS: 1
REF: 17.3
7.SP.7.a | 7.SP.7.b | 7.SP.8.a | 7.SP.8.b
TOP: Standardized Test
compound event
C
PTS: 1
REF: 16.4
NAT: 7.SP.5 | 7.SP.6 | 7.SP.7.a | 7.SP.7.b
Standardized Test
KEY: simulation | trial
C
PTS: 1
REF: 16.3
NAT: 7.SP.5 | 7.SP.6 | 7.SP.7.a | 7.SP.7.b
Standardized Test
KEY: theoretical probability
Outcome
Spade
Heart
Diamond
Club
Probability
b.
This is a non-uniform probability model because the probabilities are not equivalent to each other.
c.
PTS: 1
REF: 17.1
NAT: 7.SP.7.a | 7.SP.7.b
TOP: Pre Test
KEY: probability model | uniform probability model | non-uniform probability model
14. ANS:
a.
There are 8 possible outcomes.
b.
{A, B, C, D, 1, 2, 3, 4}
c.
Outcomes: A, B, C, D, 1, 2, 3, 4
d.
Outcomes: B, C, D, 1, 3
PTS: 1
REF: 16.1
NAT: 7.SP.5
TOP: Pre Test
KEY: outcome | experiment | sample space | event | simple event | probability | equally likely
15. ANS:
a.
{heads, tails}
b.
heads: 25 times
tails: 25 times
c.
d.
Side
e.
Tally
Total
Heads
23
Tails
27
Probability
The probabilities are different. Experimental probability is determined from doing an experiment. You
may not always get the same results as what is expected from the theoretical probability when you do an
experiment.
PTS: 1
REF: 16.2
NAT: 7.SP.5 | 7.SP.6 | 7.SP.7.a | 7.SP.7.b
TOP: Pre Test
KEY: experimental probability
16. ANS:
a.
club, diamond, heart, spade
b.
I will use 1 and 4 because there are four suits in a deck of cards.
c.
It would be better to simulate 100 trials. The experimental probability approaches the theoretical
probability as the number of trials increases.
PTS: 1
TOP: Pre Test
17. ANS:
a.
b.
c.
REF: 16.5
KEY: spreadsheet
NAT: 7.SP.6 | 7.SP.7.a | 7.SP.7.b
The possible outcomes are CCC, CCW, CWC, CWW, WCC, WCW, WWC, and WWW.
Number of Questions
Answered Correctly
0
1
2
3
Probability
d.
P (at least 2 correct)  P(2 or 3) 
e.
The complement of the event “guessing the correct answer to all three questions” is “guessing the correct
answer to 0, 1, or 2 questions.”
or
P(0, 1, or 2)  P(0)  P(1) + P(2) 
P(0, 1, or 2)  1  P(3) 
PTS: 1
REF: 17.2
NAT: 7.SP.7.a | 7.SP.7.b | 7.SP.8.a | 7.SP.8.b
TOP: Pre Test
KEY: tree diagram | complementary events
18. ANS:
a.
(R, R), (R, B), (R, P), (R, Y)
(B, R), (B, B), (B, P), (B, Y)
(G, R), (G, B), (G, P), (G, Y)
b.
There are 2 outcomes for this event: (R, R) and (B, B).
P(same color) 
c.
, or
There is 1 outcome for this event: (R, P).
P(R on 1st and P on 2nd) 
d.
There are 6 outcomes for this event: (R, R), (R, B), (R, P), (R, Y), (B, P), and (G, P).
P(R on 1st or P on 2nd) 
PTS: 1
TOP: Pre Test
, or
REF: 17.3
NAT: 7.SP.7.a | 7.SP.7.b | 7.SP.8.a | 7.SP.8.b
KEY: compound event