Question 1

Which region is shaded in the first Venn diagram (Image 1) if it represents the complement of event $$A (i.e$$., $$A^C$$)?

Accepted Answer

The area outside circle $$A$$, but inside the rectangle $$S.$$

Question 2

In the second Venn diagram (Image 2), which region represents the intersection $$A \cap B$$?

Accepted Answer

The area inside both circles $$A$$ and $$B ($$the overlapping region).

Question 3

In the fourth Venn diagram (Image 4), what does the lack of overlap between circles $$A$$ and $$B$$ indicate?

Accepted Answer

Events $$A$$ and $$B$$ are mutually exclusive.

Question 4

Which symbolic operation is represented by the union of events $$A$$ and $$B in a $$Venn diagram?

Accepted Answer

$$A \cup B$$

Question 5

Given the histogram in the last image, what is the probability $$P(X = 30)$$?

Accepted Answer

$$0.5$$

Question 6

If the histogram in the last image represents a probability distribution, what is the probability $$P(10 \u003c X \leq 30)$$?

Accepted Answer

$$0.7$$

Question 7

Which of the following best describes the event $$A^C \cap B in a $$Venn diagram?

Accepted Answer

The region inside $$B$$ but outside $$A.$$

Question 8

If $$A$$ and $$B$$ are mutually exclusive events, what is $$P(A \cap B)$$?

Accepted Answer

$$0$$

Question 9

Given the histogram, what is the sum of all probabilities shown?

Accepted Answer

$$1.0$$

Question 10

Which of the following is true about the complement of event $$A$$, denoted $$A^C$$?

Accepted Answer

It contains all outcomes not in $$A.$$

Question 11

If $$P(A) = 0.3$$ and $$P(A^C) = 0.7$$, what is $$P(S)$$, where $$S is $$the sample space?

Accepted Answer

$$1$$

Question 12

If $$A$$ and $$B$$ are events in a sample space $$S$$, which formula correctly expresses the probability of their union?

Accepted Answer

$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

Question 13

Which of the following is a valid probability distribution for a random variable $$X$$ with possible values $$1, 2, 3$$?

Accepted Answer

$$P(X=1)=0.2, P(X=2)=0.3, P(X=3)=0.5$$

Question 14

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$ and $$A$$ and $$B$$ are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$0.9$$

Question 15

Which of the following best describes the event $$(A \cup B)^C$$?

Accepted Answer

All outcomes not in $$A$$ and not in $$B.$$

Probability Concepts and Applications in Business Calculus

Study Guide - Practice Questions