Q: A company wants to compare two candies out of 86 varieties. How many different pair-wise comparisons are possible?

$$\frac{86 \times 85}{2} = 3655$$

Question 1

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

Accepted Answer

A collection of all possible outcomes of an experiment.

Question 2

Suppose a fair die is rolled. What is the probability of observing an even number?

Accepted Answer

$$\frac{1}{2}$$

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 (either 'Increase productivity' or 'Stay competitive')?

Accepted Answer

$$\frac{47 + 38}{100} = 0.85$$

Question 4

If the probability of event $$A is$$ $$0.3$$, what is the probability of the complement of $$A$$?

Accepted Answer

$$1 - 0.3 = 0.7$$

Question 5

In the context of rolling a die, let $$A = \{2, 4, 6\}$$ and $$B = \{1, 2, 3\}. $$What is $$A \cap B$$?

Accepted Answer

$$\{2\}$$

Question 6

A business is randomly selected from the diversity training table. What is the probability that 'Social responsibility' is NOT the primary reason?

Accepted Answer

$$1 - 0.04 = 0.96$$

Question 7

If an experiment consists of flipping a coin and rolling a die, how many sample points are in the sample space?

Accepted Answer

$$2 	imes 6 = 12$$

Question 8

In the two-way table of age and income, what is the probability that a randomly selected respondent is under 30 years old and has an income over $50,000?

Accepted Answer

$$0.10$$

Question 9

Which of the following statements about probabilities is TRUE?

Accepted Answer

The probability of any event is always between 0 and 1, inclusive.

Question 10

A company wants to compare two candies out of 86 varieties. How many different pair-wise comparisons are possible?

Accepted Answer

$$\frac{86 	imes 85}{2} = 3655$$

Question 11

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

$$0.4 + 0.5 = 0.9$$

Question 12

A simple event is best described as:

Accepted Answer

An event containing only a single sample point.

Question 13

In a study, 10 males and 10 females are sampled for each of three social media platforms. What is the probability that a randomly selected user is a female who uses Twitter most often?

Accepted Answer

$$\frac{10}{60} = 0.167$$

Question 14

Which of the following is the correct formula for the probability of the union of two events $$A$$ and $$B$$?

Accepted Answer

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

Question 15

If the probability of a sample point is $$0.2$$, which of the following could be a valid probability for another sample point in the same experiment?

Accepted Answer

$$0.5$$

Question 16

Which Venn diagram region represents $$A \cap B$$?

Accepted Answer

The region where circles $$A$$ and $$B$$ overlap.

Question 17

If $$P(A) = 0.6$$ and $$P(A^c) = x$$, what is the value of $$x$$?

Accepted Answer

$$0.4$$

Question 18

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.

Chapter 3: Probability – Study Notes for Business Statistics

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