AnswersSS Integrated Math IIB 2026Theoretical and Experimental Probability

Theoretical and Experimental Probability — Unit test Answers

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1
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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
2
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Which statements are true? Select three options.

A
P(F|C) = 0.75
B
P(C|F) = 0.25
C
P(C∩F) = 0.09
D
P(C∩F) = P(F∩C)
E
P(C|F) = P(F|C)
3

There are 5 customers currently present in a coffee shop. Three of the customers are waiting in line at the front register. How many different lines of customers are possible?

6
6
1
10
6
60
1
120
4

At a high school, students can choose between three art electives, four history electives, and five computer electives. Each student can choose two electives.What is the approximate probability that a student chooses a computer elective and an art elective?

A
0.11364
B
0.21212
C
0.22727
D
0.42424
5

The spinner is equally likely to land on any of the five sections.

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
6

How many 2-letter combinations can be created from the distinct letters in the word “mathematician”? Assume that the order of the letters does not matter.

A
28
B
56
C
78
D
156
7

three

S
S = {1, 2, 3, 4, 5, 6}
I
If A is a subset of S, A could be {0, 1, 2}.
I
If A is a subset of S, A could be {5, 6}.
I
If a subset A represents the complement of rolling a 5, then A = {1, 2, 3, 4, 6}.
I
If a subset A represents the complement of rolling an even number, then A = {1, 3}.
8

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
9

Ariana, Boris, Cecile, and Diego are students in the service club. Three of the four students will be chosen to attend a conference.Which choice represents the sample space, S, for this event?

A
S = {ABC, ABD, ACD, BCD}
B
S = {ABC, BCA, CDA, DAC}
C
S = {ABC, ABD, BAC, BDA, ACD, ADC, BCD, BDC}
D
S = {ABC, ABD, ACD, BCA, BCD, BDC, CAB, CBD, DAC, DBC}
10

Hana has a bag containing one red (R), one blue (B), and one yellow (Y) tile. She draws two tiles out of the bag, one after the other. Which explanation and tree diagram represent a pair of dependent of events?

A
Once a tile is chosen, it can be chosen again:
Option A
B
Once a tile is chosen, it cannot be chosen again:
Option B
C
Once a tile is chosen, it cannot be chosen again:
Option C
D
Once a tile is chosen, it can be chosen again:
Option D
11

Which best describes independent events?

A
The results of all events have different individual probabilities.
B
The results of any previous events affects the probability of future events.
C
The results of all events have the same individual probability.
D
The results of all previous events do not affect the probability of future events.
12

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.
13

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).
14

Events X and Y are independent. The probability of X occurring is . The probability of Y occurring is . What is P(X and Y)?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
15

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

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