Lesson 2.1.1
2-8. Joyce’s dad packs her lunch and always packs a yogurt. Joyce knows that there are
five yogurts in the refrigerator: one raspberry, two strawberry, one blueberry, and one
vanilla. Her dad usually reaches into the refrigerator and randomly grabs a yogurt.
a. Which flavor is she most likely to have in her lunch today? [ Strawberry ]
b. What are her chances of finding a vanilla yogurt in her lunch bag?[ 1/5 ]
2-9. A bag of marbles contains only the colors red and green.
a. If the probability of getting a red marble is 1
3 , what is the probability of getting a
green marble? [ 2/3 ]
b. If there are 24 marbles in the bag, how many are green? [ 16 ]
2-10. The Giant Prize Wheel at the county fair is evenly divided into 10 sections. One is
labeled “Large Prize,” three are labeled “Small Prize,” and the rest are labeled
“No Prize.”
a. If you spin once, what is the probability of winning a large prize? [ 1/10 ]
b. If you spin once, what is the probability of winning any prize? [ 4/10 = 2/5]
c. If 50 people spin the prize wheel, approximately how many people should expect to win a prize of any kind? [ 20 people ]
2-11. Multiple Choice: Which of the following numbers could not represent a probability?
Write a sentence explaining why. [ A; probabilities cannot be negative as there is
no probability less than 0, which represents impossibility. ]
A. - 1 / 10 B. 1 C. 1% D. 0.1
2-12. A bag contains 4 brown marbles, 3 green marbles, 2 red marbles, and 1 purple
marble. Calculate the probability of drawing each color, and write each answer as a
fraction, as a percent, and as a decimal.
P(Brown) = 4/10 = 2/5= 40%= 0.4 ,
P(Green) = 3/10 = 30%= 0.3 ,
P(Red) = 2/10 = 1/5 = 20%= 0.2 ,
P(Purple) = 1/10 = 10%= 0.1
2-13. Jessica wants to make a spinner that has all of the following characteristics. Sketch a possible spinner for Jessica. Be sure to label the sections of the spinner with a name and their theoretical probability.
The blue section is 1/6 ,
the red section is 1/3 ,
the green section is 1/8
and the purple section is 3/8 .
- Blue, red, purple and green are the only colors on the spinner.
- It is half as likely to land on blue as to land on red.
- It is three times as likely to land on purple as green.
- There is a 50% probability of landing on either blue or red and a 50%
probability of landing on either purple or green.
Lesson 2.1.2
2-22. Write “theoretical” or “experimental” to describe the probabilities for each of the
following situations.
a. The chance of getting tails when flipping a coin is 1/2 . [ T ]
b. I flipped a coin eight times and got heads six times, so the probability is 6/8 . [ E ]
c. My mom packed my lunch three of the past five days, so the probability of my
mom packing my lunch is 3/5 . [ E ]
d. The chance of winning the state lottery is 1 in 98,000,000. [ T ]
e. Based on mathematical models, the chance of rain today is 60%. [ T ]
f. Lena got three “hits” in her last seven times at bats, so her chance of getting a hit is 3/7 . [ E ]
2-23. Imagine that you have a bag containing 10 marbles of different colors. You have
drawn a marble, recorded its color, and replaced it fifty times with the following
results: 9 purple, 16 orange, 6 yellow, and 19 green marbles. Make a prediction for
how many marbles of each color are in the bag. Show all of your work or explain
your reasoning. [ Most credible prediction: 2 purple, 3 orange, 1 yellow, 4 green ]
2-24. A fair number cube with the numbers 1, 2, 3, 4, 5, and 6 is rolled.
a. What is the probability of getting an even number? [ 3/6 = 1/2 ]
b. What is the probability of getting a factor of 6? [ 4/6 = 2/3 ]
2-25. Write “theoretical” or “experimental” to describe the probabilities in each of the
following statements.
a. The chance of spinning a four on a spinner numbered one through four is 1/4 . [ T ]
b. I drew ten cards out of a deck and got hearts three times, so the chance of getting a heart is 3/10 . [ E ]
c. I made eight out of the last ten free throws, so my chance of making a free throw is 80%. [ E ]
d. The chance of winning a new car in the raffle is 1 in 32,000. [ T ]
e. Based on mathematical models, the chance of a thunderstorm today is 40%. [ T ]
2-26. Kirk is helping his grandparents set up their new portable music players. His
grandmother, Maude, has 1 jazz album, 2 country-western albums, and 5 heavy-metal
albums. Kirk’s grandfather, Claude, has 3 classical albums, 2 rap albums, and 7 heavy-metal albums.
If Kirk’s grandparents’ portable music players are on random shuffle mode, who has
the greater chance of listening to a heavy-metal album? Explain how you know.
[ Maude’s probability is 5 out of 8 while Claude’s is 7 out of 12. Reasoning may
vary, but the grandmother has a greater probability. ]
2-27. Kirk’s grandparents are really enjoying their portable music players and have
downloaded many more albums. Maude now has 225 albums, 135 of which are
heavy metal. Claude now has 450 albums, 270 of which are heavy metal. Which of
Kirk’s grandparents has a higher probability of listening to heavy metal?
[ The probabilities are the same at 60%. ]
2-28. A fair number cube labeled 1, 2, 3, 4, 5, and 6 is rolled 100 times. About how many times would you expect the number 3 to appear? [ 16 or 17 times ]
2-29. For each of the experimental results described, write the indicated probability.
a. A coin is flipped 80 times. It lands tails 47 times. What is the P(heads)? [ 33/80 ]
b. A bag contains purple and orange marbles. Sam randomly takes out one marble
then returns it to the bag. He does this 18 times, and 12 of those times an orange
marble is pulled out. What is P(green)? [ 0 ]
c. Sarah pulls a card from a standard deck and then replaces it. She does this
30 times, and 40% of the time it is hearts. What is the probability she does not
get hearts? [ 60% or 18/30 ]
Lesson 2.1.3
2-35. Tom keeps all his favorite marbles in a special leather bag. Right now the bag holds
five red marbles, four blue marbles, and three yellow marbles.
a. If he randomly chooses one marble to give to a friend, what is the probability
that it is blue? [ 4/12 = 1/3 ]
b. Tom does not really want to give away blue marbles and would like to change
the probability that he chooses a blue marble to 1/10 . How many marbles that are
not blue could he add to the bag so that the probability of choosing a blue marble
becomes 1/10 ? [ 28 ]
2-36. Your team is in charge of games at the CPM Amusement Park. One of the games
involves a robotic arm that randomly grabs a stuffed animal out of a large bin.
You need to set up the game so that the probability of a customer grabbing a teddy
bear is exactly 1/2 .
a. How would you set up the bin? Explain.
[ Make sure that half of the stuffed animals are teddy bears. ]
b. What if you returned to check on the bin and found that there were four teddy
bears left and 12 other animals. What could you add to or remove from the bin
to return the probability of selecting a teddy bear to 1/2 ?
[ Possible response: Add 8 teddy bears. ]
2-37. The probability of getting a white marble from a bag is 1/5 . If there are four white
marbles in the bag, what is the total number of marbles in the bag? [ 20 ]
2-38. Kandi has a bag of marbles. She has 5 black, 3 white, 2 green, and 4 orange marbles.
Kandi reaches into the bag without looking and pulls out a marble.
a. What is the probability that she will pull out a green marble?
[ 2/14 = 1/7 ]
b. If she does get a green marble and does not put it back in the bag, what is the
probability that she will now pull the other green marble from the bag?
[ 1/13 ]
c. Assume that Kandi does get the second green marble and does not return it to the
bag. What is the probability that she will now pull another green marble from
the bag? [ 0 ]
2-39. Jack has 120 songs on his music player. Some are rock, some are jazz, and the rest
are classical pieces. If his music player is on random shuffle mode, the probability
that it will play a classical piece is 2/5 and the probability that it will play a jazz piece
is 1/3 . How many songs of each type are on Jack’s music player?
[ 48 classical, 40 jazz, 32 rock ]
Lesson 2.1.4
2-46. What is the probability of getting either blue or green on a spinner that is 3/10 green and 1/5 blue? Show your work. [ 5/10 or 1/2 or 50% ]
2-47. If you were to spin the spinner at right, what would be the probability of landing on green or purple? Explain how you know. [ 3/4 ; Explanations vary ]
2-48. Mr. Hill has a deck of math flashcards that includes addition, subtraction, and
multiplication problems. Twenty-five cards show addition problems, 30 are
subtraction problems, and 45 are multiplication problems.
a. What is the probability of drawing a card with an addition or subtraction problem on it? [55/100=11/20 ]
b. If Mr. Hill adds 40 division flashcards to the deck, what will P(division) be?
[ 40/140 = 27 ]
c. In the new deck, which is greater: the probability of drawing an addition or
subtraction flashcard, or the probability of drawing a multiplication or division flashcard? Justify your conclusion.
[ P(+ or -) = 55/140 = 11/28 , drawing multiplication or division is more likely. ]
2-49. Erica is making a quilt like the one shown at right. She is going to
give each square to a different person to decorate before she sews
them together.
a. If she gives people squares at random, what is the probability
that she will give her mother a gray square to decorate?
b. What is the probability that she will give her brother a gray or a black square to
decorate? [ a: 12/30 = 2/5, b: 20/30 = 2/3 ]
Lesson 2.1.5
2-58. Multiple Choice: If the probability of getting a particular result in an experiment is
75.3%, what is the probability of not getting that result? Explain your choice.
A. 75.3% +100% B. 75.3% -100%
C. 100% - 75.3% D. 1/75.3%
[ C ]
2-59. Thu has a bag with 7 green marbles, 5 blue marbles, and 4 red marbles. For each part
below, if the marble selected is replaced before the next marble is drawn, what is the
probability that she will draw:
a. A red marble?
b. A red or a green marble?
c. An orange marble?
[ a: 4/16 or 1/4 , b: 7/16 + 4/16 = 11/16 , c: 0 ]
2-60. Lila is making a spinner game for her cousins to play. She has divided it into 8 equal sections, and has labeled each one with a symbol. When the spinner lands on a flower (✿), her cousins will win a prize.
a. What is P(★)? [ 3/8 ]
b. What is the probability of not getting ♦? [ 1 - 1/8 = 7/8 ]
c. What is P(✿)? [ 2/8 = 1/4 ]
d. If Lila’s cousins spins 100 times, about how many times would you expect them
to spin a heart (♥)? [ 25; Sample reasoning: 1/4 of the spaces are hearts, and
25 times would be 1/4 of 100. OR There are 2/8 hearts, and 8 goes into 100
just more than 12 times. So, since 2 * 12 = 24 , about 25 times. ]
2-61. A box of candy holds 36 pieces. Sixteen pieces in the box are caramels, three pieces
are marshmallow chews, five pieces are fruit centers, eight pieces are nut clusters, and
the rest are white chocolate.
a. What is the probability of randomly choosing a caramel out of the box? [ 16/36 = 4/9 ]
b. What is the probability that you will not choose a fruit center or a nut cluster? [ 23/36 ]
c. In a different box, there is a 16 chance that you will choose a fruit center. From
which box is it more likely that you will choose a fruit center?
[ It is more likely to get a fruit center from the new box, because 1/6 5/36 . ]
2-62. John has a bag of marbles that contains 12 red marbles, 20 green marbles, and 17 blue marbles.
a. If John pulls one marble out of the bag, what is the probability that it will not be red, that is, P(not red) ?
[ 37 out of 49 ]
b. What is the probability that he will draw a purple marble, that is, P(purple) ?
[ 0 out of 49, there are not any purple marbles in the bag. ]
2-63. Linh has a bag of beads that contains 10 glass beads, 7 metal beads, 15 plastic beads, and 3 clay beads. For each part below, if the bead selected is replaced before the next draw, what is the probability that she will pull out a:
a. Metal bead? [ 7/35 = 1/5 ]
b. Bead that is not plastic? [ 20/35 = 4/7 ]
c. Glass or plastic bead? [ 25/35 = 5/7 ]
http://www.cpm.org/pdfs/standards/stats/Stats%20Unit%202%20TV.pdf