Q: Given the table of primary reasons for diversity training, what is the probability that a randomly selected business cites a business-related reason (Increase productivity or Stay competitive)?

$P(\text{Business-related}) = \frac{47 + 38}{100} = 0.85$

Q: A couple has two children. What is the probability that both are girls, assuming each child is equally likely to be a girl or boy?

$P(\text{two girls}) = 0.5 \times 0.5 = 0.25$

Q: Given the table of primary reasons for diversity training, what is the probability that social responsibility is NOT the primary reason?

$P(\text{not SR}) = 1 - \frac{4}{100} = 0.96$

Q: If you flip a fair coin three times, what is the probability of getting exactly two heads?

$P(\text{exactly 2 heads}) = \frac{3}{8}$

Question 1

Which of the following best describes a sample space in probability theory?

Accepted Answer

A collection of all possible outcomes of an experiment.

Question 2

Suppose you roll a fair six-sided die. What is the probability of observing an even number?

Accepted Answer

$P(A) = \frac{3}{6} = 0.5$

Question 3

Given the table of primary reasons for diversity training, what is the probability that a randomly selected business cites a business-related reason (Increase productivity or Stay competitive)?

Accepted Answer

$P(	ext{Business-related}) = \frac{47 + 38}{100} = 0.85$

Question 4

If the probability of event $A$ is $0.4$, what is the probability of its complement $A^c$?

Accepted Answer

$P(A^c) = 1 - 0.4 = 0.6$

Question 5

Which of the following is a compound event?

Accepted Answer

Observing an even number when rolling a die.

Question 6

If $A$ and $B$ are two events, which formula represents the probability of the union of $A$ and $B$?

Accepted Answer

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

Question 7

A couple has two children. What is the probability that both are girls, assuming each child is equally likely to be a girl or boy?

Accepted Answer

$P(	ext{two girls}) = 0.5 	imes 0.5 = 0.25$

Question 8

Which of the following statements about probabilities is TRUE?

Accepted Answer

The sum of the probabilities of all sample points in a sample space is 1.

Question 9

Suppose the probability of observing a number less than or equal to 3 when rolling a fair die is $P(B)$. What is $P(B)$?

Accepted Answer

$P(B) = \frac{3}{6} = 0.5$

Question 10

Given the table of primary reasons for diversity training, what is the probability that social responsibility is NOT the primary reason?

Accepted Answer

$P(	ext{not SR}) = 1 - \frac{4}{100} = 0.96$

Question 11

If you flip a fair coin three times, what is the probability of getting exactly two heads?

Accepted Answer

$P(	ext{exactly 2 heads}) = \frac{3}{8}$

Question 12

Which Venn diagram correctly represents the intersection of two events $A$ and $B$?

Accepted Answer

The diagram where only the overlapping region between $A$ and $B$ is shaded.

Question 13

Which of the following is NOT a valid probability rule for sample points?

Accepted Answer

The probability of a sample point can be greater than 1.

Question 14

Suppose you roll a fair die. Let $A$ be the event 'toss an even number' and $B$ be the event 'toss a number less than or equal to 3'. What is $A \cap B$?

Accepted Answer

$A \cap B = \{2\}$

Question 15

If the probability of observing a head when flipping a fair coin is $p_1$ and the probability of observing a tail is $p_2$, which of the following is correct?

Accepted Answer

$p_1 + p_2 = 1$

Question 16

Which of the following best describes the complement of an event $A$?

Accepted Answer

The event that $A$ does not occur.

Question 17

A business is randomly selected from those that use diversity training. What is the probability that the primary reason is 'Other'?

Accepted Answer

$P(	ext{Other}) = \frac{4}{100} = 0.04$

Question 18

If $P(A) = 0.3$ and $P(B) = 0.5$ and $P(A \cap B) = 0.1$, what is $P(A \cup B)$?

Accepted Answer

$P(A \cup B) = 0.3 + 0.5 - 0.1 = 0.7$

Chapter 3: Probability – Foundations and Operations

Study Guide - Practice Questions

Study Guide - Flashcards