Name: _________________________________________ Date: _________ Score: ______ / 20
What Do You Expect Assessment
Short Answer: Answer each question, making sure to show your work or provide an explanation or sketch to support
your answer in the box.
1.
(1 point)
Michelle flips a penny four times, and it lands heads up all four times. On her fifth
flip, what is the probability that the penny will land tails up? Explain your reasoning.
2.
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 4-sided 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.
• The player with the most points after 32 rolls wins.
a.
(1 point)
Make a table that shows all the possible outcomes of rolling two 4-sided
number cubes.
b.
(0.5 point)
What is the probability of rolling a sum of 5?
c.
(0.5 point)
What is the probability of rolling a sum of 4?
d.
(1 point)
Do you think the game is fair? Explain your reasoning.
e.
(1 point)
Suppose that, in 32 rolls, a sum of 8 is rolled twice. Would you consider
this unusual? Explain your reasoning.
Region
Number of times
spinner lands in region
1
9
2
4
3
12
4
11
3.
Evan has a spinner that is divided into four regions. He spins the spinner
several times and records his results in a table.
a.
(1 point)
Based on Evan’s results, what is the probability of the spinner landing on
each region?
b.
(1 point)
Are the probabilities you found in parts (a) theoretical probabilities or
experimental probabilities? How do you know?
f.
(1 point)
Make a drawing of what Evan’s spinner might look like.
4.
Suppose the Crawfords have three children. Assume that the probability
of a boy or a girl is for each birth.
a.
(1 point)
`List the possible outcomes.
b.
(0.5 point)
What is the probability that exactly two of the Crawfords’ children are
boys and the boys are born in a row?
c.
(0.5 point)
What is the probability that the Crawfords have at least two boys born in
a row?
d.
(1 point)
Explain why the answers to parts (b) and (c) are not the same.
5.
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. (1 point)
Tua spins spinner A once and spinner B once. What is the probability she
will get green? Explain.
b.
(1 point)
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.
____ 6.
(1 point)
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?
a.
3
b.
6
c.
9
d.
12
____ 7.
(1 point)
The probability of rolling a 6 on a regular number cube is . If Jacob tosses a number
cube 24 times, how many times would he expect to roll a 6?
a.
2
b.
4
c.
3
d.
5
____ 8.
(1 point)
What is the probability of spinning a multiple of 4 on this spinner?
a.
b.
c.
d.
____ 9.
(1 point)
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.
(1, 3)
b.
(3, 3)
c.
(3, 2)
d.
(3, 4)
____ 10.
(1 point)
A bag contains 5 red marbles, 4 white marbles, and 9 blue marbles. You pick a marble
without looking. Find the probability of drawing a white marble.
a.
b.
c.
d.
____ 11.
(1 point)
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.
0.11
b.
0.36
c.
0.14
d.
0.64
_____ 12. (1 point)
Irene randomly tosses a cube onto the grid below. What is the probability of the cube
not landing on a dotted rectangle?
a.
85%
b.
3%
c.
17%
d.
15%