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Unit 7 Study Guide
1. Use the spinner to name the color that fits each of the following statements.
black
blue
white
black
white
green
blue
a. The spinner will land on this color about as often as it lands on white.
1
b. The chance of getting this color is .
6
c. The probability of landing on this color is greater than 30%.
2. In 12 spins, the spinner lands on green 4 times. Explain how this is possible if the spinner
should only land on green 1 out of every 6 times.
3. Answer the following questions about making random draws from a deck of five cards
numbered 1, 2, 3, 4, and 5.
a. What is the probability of drawing a number 1? Express the probability as a fraction, decimal,
and percent.
b. What is the probability of not drawing a number 1? Express the probability as a fraction,
decimal, and percent.
c. Suppose you draw the number 3. What is the probability that 3 will come up on the next draw?
Assume that the cards have no memory. Express the probability as a fraction, decimal, and
percent.
4. While making random draws from a deck of five cards numbered 1, 2, 3, 4, and 5, if you draw
a card 40 times, putting the card back and mixing the deck after each draw, about how many
times would you expect to draw the number 4?
5. Balls are dropped, one at a time, into the chute shown below. Each time the chute divides, the
ball has an equal chance of going down any of the chutes. Thirty-six balls are dropped into the
chute. Fill in the boxes in the tree diagram to show how many balls you would expect to go down
each chute.
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Unit 7 Study Guide
6. Balls are dropped, one at a time, into the chute shown below. Each time the chute divides, the
ball has an equal chance of going down any of the chutes. Seventy-two balls are dropped into the
chute. Fill in the boxes in the tree diagram to show how many balls you would expect to go down
each chute.
7. Mary and Trent designed the game Lucky Draw for their school carnival. To play, draw a card
from a standard deck of cards. Replace the card after each draw. If you draw a red card you lose.
If you draw a black card, you get to draw again. If you draw a black card on the second draw,
you win the prize. If you draw a red card on the second draw, you lose. Make a tree diagram to
help you answer the question below.
a. What is the probability of winning Lucky Draw?
b. If 108 people play Lucky Draw, how many would you expect to win?
c. Explain why this is not a fair game.
d. How would you change the rules to make Lucky Draw a fair game?
8. Steve and Christine designed the game Lucky Marble for their school carnival. To play, draw a
marble blindly from a bag with one green marble and three red marbles. Replace the marble after
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Unit 7 Study Guide
each draw. If you draw a green marble you lose. If you draw a red marble, you get to draw again.
If you draw a red marble on the second draw, you win the prize. If you draw a green marble on
the second draw, you lose. Make a tree diagram to help you answer the question below.
a. What is the probability of winning Lucky Marble?
b. If 96 people play Lucky Marble, how many would you expect to win?
c. Explain why this is not a fair game.
d. How would you change the rules to make Lucky Marble a fair game?
9. The Venn diagram below shows the number of students in Mr. Penn’s class that have a dog, a
cat, or both. Use the diagram to answer the following questions.
a. How many students have a dog?
b. How many students have a cat but not a dog?
c. How many students have both a cat and a dog?
d. How many students are represented in the diagram?
dogs cats
12
6
3
10. The Venn diagram below shows the number of students in Mr. Penn’s class that have a dog,
a cat, or both. Use the diagram to answer the following questions.
a. How many students have a dog?
b. How many students have a cat but not a dog?
c. How many students have both a cat and a dog?
d. How many students are represented in the diagram?
dogs cats
8
4
5
11. Suppose a coin is tossed at random onto the gameboard shown below. What is the probability
22
that it will land inside the circle? Use
for  . Express your answer as a fraction and a
7
percent.
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Unit 7 Study Guide
18 in.
8 in.
Solve each equation.
12. 3x  3  x  9
13.
FG 19 IJ y  38  FG 17 IJ y – 34
H 9K
H 9K
Solve each equation.
14.
FG 14 IJ y  28  FG 13IJ y – 26
H 5K
H 5K
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Unit 7 Study Guide
[1] a. blue
b. green
c. black
[2] Sample answer: The actual results, in a small sample of trials, is often very different from the
expected probability. The more trials that are done, the closer the results will be to the expected
probability.
[3] a.
1
, 0.2, 20%
5
4
, 0.8, 80%
5
1
c. , 0.2, 20%
5
b.
[4] 8 times
[5]
36
18
9
18
9
[6]
6
6
6
72
36
18
36
18
12
12
12
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Unit 7 Study Guide
[7]
26
52
26
52
black
26
52
red
26
52
black
win prize
red
1
4
b. 27 people
c. Sample answer: The chances of winning and losing are not equal.
d. Sample answer: If you draw a red card, you win.
a.
[8]
3
4
1
4
red
3
4
red
win prize
green
1
4
green
9
16
b. 54 people
c. Sample answer: The chances of winning and losing are not equal.
d. Sample answer: If you draw a green marble, you win.
a.
[9] a. 18 students
b. 3 students
c. 6 students
d. 21 students
[10] a. 12 students
b. 5 students
c. 4 students
d. 17 students
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Unit 7 Study Guide
[11]
352
; 62.08%
567
[12] 3
[13] Solution: y  18
[14] Solution: y  10