Name:
What Do You Expect Practice Test (INTRO)
Short Answer
1. To help his 3-year-old sister Emily learn her colors, Kyle has put some yellow, green, red, and blue
blocks in a bucket. Emily draws a block from the bucket, names its color, and puts the block back in
the bucket. Then Kyle mixes the blocks, and Emily draws again. In playing this game 20 times, Emily
draws a yellow block 6 times, a green block 2 times, a red block 8 times, and a blue block 4 times.
a. Based on Emily’s draws, what is the probability of drawing a yellow block from the bucket?
b. What is the probability of drawing a green block from the bucket?
c. What is the probability of drawing a red block from the bucket?
d. What is the probability of drawing a blue block from the bucket?
e. Are the probabilities you found in parts (a)–(d) experimental probabilities or theoretical
probabilities? Explain your reasoning.
f.
There are a total of 10 blocks in the bucket. Based on the results of Emily’s 20 draws, how
many yellow, green, red, and blue blocks would you expect to be in the bucket? Explain your
reasoning.
2. a. If a letter is randomly selected from the letters A, B, C, D, and E, what is the probability that the
letter will be B? Explain your reasoning.
b. If a letter is selected by spinning the spinner below, what is the probability that the letter will be B?
Explain your reasoning.
c. Are your answers to parts (a) and (b) the same? Explain why or why not.
d. If the spinner is spun once, what is the probability that it will not land in region C? Explain your
reasoning.
e. If the spinner is spun once, what is the probability that it will land in region D? Explain your
reasoning.
f.
If the spinner is spun 100 times, how many times would you expect it to land in region E? Explain
your reasoning.
3. 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?
b. What is the probability of rolling a sum of 6?
c. What is the probability of rolling a sum of 4?
d. What is the probability of rolling a sum that is not 1 or 6? Explain your reasoning.
4. Jennifer is on her school’s softball team. So far this season, Jennifer has 38 hits in 75 times at bat.
a. Based on her current batting average, what are Jennifer’s chances of getting a hit next time
she is at bat? Explain your reasoning.
b. If Jennifer bats 5 times during a game, how many hits would you expect her to get? Explain
your reasoning.
c. Next season, Jennifer wants to average 6 hits for every 10 times at bat. If she bats 80 times
during the season, how many hits will she need to get to achieve her goal?
5. Two identical containers contain marbles. Container 1 has 2 white marbles and one red marble.
Container 2 has one white marble and one red marble. If you select a container at random and then
draw out a marble, what is the probability of drawing a white marble?
6. Tua has created a new game called Making Green. To play the game, a player spins twice. If the
player gets blue in one section and yellow in the other, the player wins, because blue and yellow
together make green. The player can choose either spinner for either of their two spins.
a. Tua spins spinner A once and spinner B once. What is the probability she will get green?
Explain.
b. Is there a different choice of selecting the spinners to make the probability of making green
greater than that in part (a)? Explain your reasoning.
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
7. Candice is the best hitter on her high school softball team. She gets on base safely 60% of the time.
What is the probability that her next at bat will result in her getting on base?
a.
____
b.
8. What is the probability of spinning a multiple of 4 on the spinner below?
a.
____
b.
9. A spinner that has 3 sections of equal area, numbered from 1 to 3, is spun two times in succession.
Which is NOT part of the sample space?
a. (3, 4)
b. (3, 3)
____ 10. Find the sample space for tossing 2 coins. Then find P(exactly 1 head).
a.
1
2
b. 1
4
A game involves spinning this spinner.
____ 11. What is the probability of the pointer landing on G?
a.
5
8
b.
1
8
____ 12. A number cube is rolled 360 times and the results are recorded as follows: 60 ones, 58 twos, 70
threes, 74 fours, 38 fives, and 60 sixes. What is the experimental probability of rolling a two or a
three?
a. 0.36
b. 0.14
What Do You Expect Practice Test
Answers
1.
a.
b.
c.
d.
e. These are experimental probabilities. We do not know how many of each color are in the bag so
the probabilities are based only on the experiment of drawing out blocks.
f. 3 yellow, 1 green, 4 red and 2 blue. These numbers would make the theoretical probability match
the calculated experimental probabilities.
2. a.
, assuming that each letter is equally likely. If we do not assume this, we do not know what the
probabilities are.
b.
. This is the portion of the spinner occupied by the region marked B.
c. The answers are not the same. It is clear in part (b) that the probabilities of the various letters are
not equal.
d.
e.
3. a.
f. We would expect this to happen about 33 times, since 33 is about
b.
d.
=
c.
. There are three ways to get a 1 and one way to get a 6. There are 32 ways to get neither
one. 1 – P(1) – P(6) = 1 –
4. a.
b. about 3, since
5. P(White) =
6.a.
of
=
+
–
=
is a little bit more than
of
=
.c. 48
.
.
b. Spinning spinner A twice gives a probability of making green as
twice gives a probability of making green as
or
or
. Spinning spinner B
. So there is no way to do better than by
spinning each spinner once.
MULTIPLE CHOICE
7.A
8.A
of 100.
9.A
10.A
11.B
12.A