Download What Do You Expect? Study Guide--key

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What Do You Expect? Study Guide--key
1. A bag contains two green marbles, four yellow marbles, six blue marbles, and eight red
marbles. Draws of marbles are made randomly.
a. What is the probability of drawing a blue marble?
b. What is the probability of not drawing a blue marble?
c. If you double the number of green, yellow, blue, and red marbles in the bag, what will be
the probability of drawing a blue marble?
d. How does your answer to part (c) compare with your answer to part (a)? Explain
e. If you add two of each color to the original bag of marbles, what will be the probability
of drawing a blue marble?
a.
=
b.
=
c.
=
d. The probabilities are the same.
e.
=
2. A bag contains two red marbles and two white marbles.
a. After a marble is drawn, it is replaced before the next draw. What is the probability that a
red marble will be drawn twice in a row? Explain.
a. P(2 reds) =
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3. Shawon has a spinner that is divided into four regions. He spins the spinner several times and
records his results in a table.
Region
1
2
3
4
Number of times
spinner lands in region
9
4
12
11
a. Based on Shawon’s results, what is the probability of the spinner landing on region 1?
b. What is the probability of the spinner landing on region 2?
c. What is the probability of the spinner landing on region 3?
d. What is the probability of the spinner landing on region 4?
e. Are the probabilities you found in parts (a)–(d) theoretical probabilities or experimental
probabilities?
a.
b.
c.
d.
e. These are experimental probabilities.
4. A 4-sided number cube is a pyramid with four faces that are congruent equilateral triangles.
The shape of a 4-sided number cube is also called a tetrahedron.
The faces of a 4-sided number cube are labeled with the numbers 1, 2, 3, and 4. A roll of a 4sided number cube is determined by the number on the face the number cube lands on. Below are
the rules of a game played with two 4-sided number cubes.
• Player I and Player II take turns rolling two 4-sided number cubes.
• If the sum of the numbers rolled is odd, Player I gets a point.
• If the sum of the numbers rolled is even, Player II gets a point.
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• The player with the most points after 32 rolls wins.
a. Make a table that shows all the possible outcomes of rolling two 4-sided number cubes.
a.
b. What is the probability of rolling a sum of 5?
c. What is the probability of rolling a sum of 4?
d. Do you think the game is fair? Explain your reasoning.
e. Suppose that, in 32 rolls, a sum of 8 is rolled twice. Would you consider this unusual?
Explain your reasoning.
b.
c.
d.
e. Yes, this game is fair. This is because even and odd sums are equally likely and each player
earns the same number of points for a win.
5. Juanita is holding five coins with a total value of 27 cents.
a. What is the probability that three of the coins are pennies? Explain your reasoning.
b. What is the probability that one of the coins is a quarter? Explain your reasoning.
a. The probability of this is zero. This is because if there are 3 pennies in the collection, the
remaining 2 coins would have to total 24 cents. This is impossible.
b. The probability of this is also zero. This is because if one of the coins is a quarter, the
remaining 4 coins would have to total 2 cents. This is impossible.
6. The faces of one six-sided number cube are labeled 1, 1, 1, 2, 2, 3, and the faces of a second cube
are labeled 0, 1, 2, 2, 2, 3. The two cubes are rolled, and the results are added.
a. What is the probability of rolling a sum of 1? 1/12
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b. What is the probability of rolling a sum of 6? 1/36
c. What is the probability of rolling a sum of 4? 5/18
7. Aaron bowls on his school’s bowling team. Based on statistics from past games, the probability that
Aaron will knock down all ten pins on his first ball (a strike) is . If he does not get a strike, the
probability that he will knock down the remaining pins with his second ball (a spare) is .
a. In bowling, a turkey is three strikes in a row. If Aaron bowls three turns, what is the
probability that he will get a turkey?
b. Aaron had 8 chances to make spares during one of his league games. How many of the spares
would you expect him to have made? Explain your reasoning.
a.
b. 6 is
of 8.
8. Suppose you play a game in which you toss 1 coin. You win $10 if it lands HEADS and you win
nothing if it lands TAILS.
a. If it costs $5 to play the game, would you expect to win or lose money in the long run? Explain
your thinking.
The player should break even in the long run. The expected value for the game is $0.00.
b. If it costs $4 to play the game, would you expect people to want to play the game? Explain your
thinking.
Everyone should play this game, since the expected value is greater than zero: winning $5.00 on
each turn versus only $4.00 to play. The expected value is $1.00. Players will come out ahead
in the long run.
9. Suppose the Crawfords have three children. Assume that the probability of a boy or a girl is
for
each birth.
a. List the possible outcomes for the genders of the three children.
b. What is the probability that exactly two of the Crawfords’ children are boys and the boys are
born in a row?
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c. What is the probability that the Crawfords have at least two boys born in a row?
d. Explain why the answers to parts (b) and (c) are not the same.
a. GGG, GGB, GBG, BGG, BBG, BGB, GBB, BBB
b.
c.
d. BBB is not “exactly two boys” so we are counting more outcomes as favorable.
Multiple Choice
On any given day, the cafeteria offers 3 main dishes for lunch (pizza, hamburger, or the featured item that
day) and 3 kinds of drinks (white milk, chocolate milk, or apple juice). How many possible choices are
there for lunch?
9
J’Mesha and Aarti each bought a gift and wanted to have it wrapped at the store. The store offers 2
designs of paper (solid or polka dots) and each design comes in 3 different colors. If the clerk chooses the
paper randomly, what is the probability that the gifts will get wrapped identically?
1/6