Q: If two events A and B are mutually exclusive, which formula should be used to find the probability that either A or B occurs?

$$P(A \text{ or } B) = P(A) + P(B)$$

Q: A restaurant offers 4 appetizers, 7 entrées, 4 desserts, and 3 drinks. How many different meals (one from each category) can be ordered?

$$4 \times 7 \times 4 \times 3 = 336$$

Q: If you draw two cards from a standard deck without replacement, what is the probability that the first card is a red queen and the second card is a red card?

$$P = \frac{2}{52} \times \frac{25}{51} = 0.0186$$

Q: If $$P(A) = 0.57$$, $$P(B) = 0.64$$, and $$P(A \text{ and } B) = 0.40$$, what is $$P(A \text{ or } B)$$?

$$P(A \text{ or } B) = 0.57 + 0.64 - 0.40 = 0.81$$

Question 1

Which of the following best describes the difference between classical, empirical, and subjective probability?

Accepted Answer

Classical probability is based on equally likely outcomes, empirical probability is based on observed data, and subjective probability is based on personal judgment.

Question 2

A company surveyed 1,025 adults about their Christmas spending. If 144 people planned to spend between $$250-499$$, what is the probability that a randomly selected person from this survey planned to spend in that range?

Accepted Answer

$$P = \frac{144}{1,025} = 0.140$$

Question 3

Which of the following values is NOT a valid probability?

Accepted Answer

$$-0.6$$

Question 4

If the probability of an employee receiving a pay cut is $$0.06$$, what is the probability that an employee did NOT receive a pay cut?

Accepted Answer

$$0.94$$

Question 5

A deck of 52 cards contains 4 kings. What is the probability of drawing a king from a well-shuffled deck?

Accepted Answer

$$P = \frac{4}{52} = 0.077$$

Question 6

Which of the following scenarios is best analyzed using subjective probability?

Accepted Answer

The probability that the price of gasoline will exceed $4.00 per gallon next summer.

Question 7

If two events A and B are mutually exclusive, which formula should be used to find the probability that either A or B occurs?

Accepted Answer

$$P(A 	ext{ or } B) = P(A) + P(B)$$

Question 8

A restaurant offers 4 appetizers, 7 entrées, 4 desserts, and 3 drinks. How many different meals (one from each category) can be ordered?

Accepted Answer

$$4 	imes 7 	imes 4 	imes 3 = 336$$

Question 9

If you draw two cards from a standard deck without replacement, what is the probability that the first card is a red queen and the second card is a red card?

Accepted Answer

$$P = \frac{2}{52} 	imes \frac{25}{51} = 0.0186$$

Question 10

Which of the following statements is TRUE about independent events?

Accepted Answer

If events A and B are independent, $$P(A|B) = P(A)$$

Question 11

A panel of 12 jurors is to be selected from a group of 50 people. How many different juries can be selected?

Accepted Answer

$$50C12$$

Question 12

In a race with 8 swimmers, how many ways can the swimmers finish first, second, and third?

Accepted Answer

$$8P3 = 336$$

Question 13

A survey of 150 households found that 34 had one television. What is the probability that a randomly selected household has one television?

Accepted Answer

$$P = \frac{34}{150} = 0.227$$

Question 14

If $$P(A) = 0.57$$, $$P(B) = 0.64$$, and $$P(A 	ext{ and } B) = 0.40$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$P(A 	ext{ or } B) = 0.57 + 0.64 - 0.40 = 0.81$$

Question 15

Which of the following is an example of a mutually exclusive event?

Accepted Answer

Drawing a spade and drawing a heart in a single card draw from a deck.

Question 16

If you toss two fair coins, what is the probability of getting exactly one head?

Accepted Answer

$$P = \frac{1}{2}$$

Question 17

Which formula is used to calculate the number of ways to arrange n objects in order, selecting r at a time?

Accepted Answer

$$nPr = \frac{n!}{(n-r)!}$$

Question 18

A contingency table shows 11 customers purchased a warranty and 49 did not, out of 60 total. What is the probability that a randomly selected customer purchased a warranty?

Accepted Answer

$$P = \frac{11}{60} = 0.183$$

Probability Concepts and Rules in Business Statistics

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