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

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