AnswersSS Integrated Math IIB 2026Probability and Two-Way Tables

Probability and Two-Way Tables — Unit test Answers

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1
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A survey was taken of children between the ages of 10 and 17 about how many siblings they have and whether they have a pet. The results of the survey are shown in the table.

Question illustration
A
Out of the 125 children who do not have a pet, 18 of them have 2 siblings.
B
Out of the 97 children who have 1 pet, 40 of them do not have any siblings.
C
Out of the 125 children who do not have any siblings, 34 of them have a pet.
D
Out of the 97 children who have 1 sibling, 40 of them do not have a pet.
2
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A burrito restaurant recorded 200 customer orders. Each order was categorized by whether it was takeout or dine-in and whether it was placed on a weekday or a weekend.The results are shown below: Using this table, decide which statement about independence is true. Which statement is correct?

Question illustration
A
The events “takeout” and “weekday” are independent.
B
The events “weekday” and “weekend” are independent.
C
The events “order type” (takeout or dine-in) and “day of the week” (weekday or weekend) are not independent.
D
The events “takeout” and “dine-in” are independent.
3

Sam kept track of the number of problems he was assigned for his math homework on the box plot.Which statement must be true according to the box plot?

Question illustration
A
The data is symmetric and shows that half of the assignments contained 15 problems or fewer.
B
The data is symmetric and shows that the majority of the assignments had 19 problems or more.
C
The data is skewed and shows that half of the assignments contained 15 problems or fewer.
D
The data is skewed and shows that the majority of the assignments had 19 problems or more.
4

The weather report states that the probability it will rain on Wednesday is 30 percent and the probability that it will rain on Saturday is 60 percent.What is the probability that it will rain on Wednesday and on Saturday?

A
2 percent
B
18 percent
C
60 percent
D
90 percent
5

Steve determined the number of states each of his friends has visited.Which statement must be true according to the box plot?

Question illustration
A
The data is skewed left and shows that half of Steve’s friends have visited 4 to 10 states.
B
The data is skewed left and shows that half of Steve’s friends have visited 10 to 40 states.
C
The data is skewed right and shows that half of Steve’s friends have visited 4 to 10 states.
D
The data is skewed right and shows that half of Steve’s friends have visited 10 to 40 states.
6

Ryder shot a model rocket over an area that consists of two grassy areas, shown in green, and an area with no grass, shown in white.

Question illustration
A
0.2
B
0.3
C
0.4
D
0.6
7

2 circles labeled Set A and Set B overlap. Set A contains 1, set B contains 3, and the overlap of the 2 circles contains 2. The number 4 is outside of the circles.

Question illustration
A
I
B
II
C
III
D
IV
8

Belleville High School offers classes on three different foreign languages. Let A be the event that a student is in eleventh grade, and let B be the event that a student is enrolled in French class.

Question illustration
A
A and B are independent events because P(A∣B) = P(A).
B
A and B are independent events because P(A∣B) = P(B).
C
A and B are not independent events because P(A∣B) ≠ P(A).
D
A and B are not independent events because P(A∣B) ≠ P(B).
9

Circle B is inside of circle A.

Question illustration
A
A = {states in the US}; B = {world countries}
B
A = {plays by Shakespeare}; B = {playwrights}
C
A = {animals}; B = {mammals}
D
A = {polygons}; B = {circles}
10

Consider the following sets.U = {all triangles}E = {x|x ∈ U and x is equilateral}I = {x|x ∈ U and x is isosceles}S = {x|x ∈ U and x is scalene}A = {x|x ∈ U and x is acute}O = {x|x ∈ U and x is obtuse}R = {x|x ∈ U and x is right}Which is a subset of I?

A
E
B
S
C
A
D
R
11

The conditional relative frequency table below was generated by column using data comparing gender and a person's favorite meal to cook.Which would most likely indicate an association between the categorical variables?

Question illustration
A
The value of A is similar to the value of B.
B
The value of A is similar to the value of E.
C
The value of B is not similar to the value of C.
D
The value of B is not similar to the value of F.
12

The manager of a grocery store reports that there is a 12 percent chance that a customer buys apples during a shopping trip, a 5 percent chance that a customer buy apples and carrots, and a 17 percent chance that a customer buys apples or carrots.What is the probability of a customer buying carrots?

A
1.4 percent
B
5.0 percent
C
10.0 percent
D
11.4 percent
13

Miriam is visiting five friends in her neighborhood, Louise, Mike, Nicole, Oscar, and Pascal. In each arrangement below, the first initial of each person’s name represents that person’s position as he or she is visited by Miriam.Which shows all the outcomes for this event if she visits with Nicole first and Louise last?

A
NMOPL, NOMPL, NPMOL
B
NLMOP, NLOMP, NMLOP, NMOLP, NOMNP, NONMP
C
NMOPL, NMPOL, NOPML, NOMPL, NPMOL, NPOML
D
NLMOP, NMLOP, NOLMP
14

A prize bag contains four country music CDs, eight pop music CDs, and five classic rock CDs.What is the probability of pulling out a classic rock CD and then, without replacing it, pulling out a country music CD? Express your answer in decimal form, rounded to the nearest hundredth.

A
0.03
B
0.07
C
0.15
D
0.18
15

Information about how the students at Vista View High School got to school this morning is shown in the table.

Question illustration
1
11
7
74
1
111
1
114

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