Q: A local pub has tracked beer purchases. Of the past 500 purchases, 120 have been for 'light' beers. What is the probability that the next beer ordered will be 'light'?

$$P(\text{light}) = \frac{120}{500} = 0.24$$

Q: If two events are mutually exclusive, which of the following statements is true?

$$P(E_1$ \text{ and } E_2$) = 0$$

Q: A company has 10 employees – 3 management and 7 staff. Two employees are selected at random to attend a conference. What is the probability that both selected are staff?

$$P(\text{both staff}) = \frac{7}{10} \times \frac{6}{9} = 0.467$$

Q: Which formula correctly expresses the addition rule for two events A and B?

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

Q: A retail clothing store has 6 pairs of style A boots, 12 pairs of style B, and 2 pairs of style C. If a clerk randomly picks one pair, what is the probability it is style A or style C?

$$P(A \text{ or } C) = \frac{6+2}{20} = 0.4$$

Q: If the probability of a company earning a profit is 0.50, breaking even is 0.30, and losing money is 0.20, what is the probability the company does NOT earn a profit?

$$P(\text{not profit}) = 1 - 0.50 = 0.50$$

Q: A small city has three airlines: 60% fly United, 30% Delta, and 10% Southwest. 70% of fliers are for pleasure, 30% for business. If airline and trip type are independent, what is the probability a flier uses Delta and is a business traveler?

$$P(\text{Delta and Business}) = 0.30 \times 0.30 = 0.09$$

Q: A golfer has 12 shirts (9 white, 3 blue). He selects one at random each day for two days, without replacement. What is the probability both shirts selected are white?

$$P(\text{both white}) = \frac{9}{12} \times \frac{8}{11} = 0.545$$

Question 1

Which of the following best describes the classical probability assessment method?

Accepted Answer

It is based on the ratio of the number of ways an outcome or event of interest can occur to the number of ways any outcome can occur, assuming all outcomes are equally likely.

$$P(E_i) = \frac{	ext{Number of ways } E_i 	ext{ can occur}}{	ext{Total number of possible outcomes}}$$

Question 2

A local pub has tracked beer purchases. Of the past 500 purchases, 120 have been for 'light' beers. What is the probability that the next beer ordered will be 'light'?

Accepted Answer

$$P(	ext{light}) = \frac{120}{500} = 0.24$$

Question 3

Which of the following is an example of subjective probability?

Accepted Answer

Estimating the likelihood that the US budget deficit will be reduced by half in the next 10 years.

Question 4

If two events are mutually exclusive, which of the following statements is true?

Accepted Answer

$$P(E_1$ 	ext{ and } E_2$) = 0$$

Question 5

A company has 10 employees – 3 management and 7 staff. Two employees are selected at random to attend a conference. What is the probability that both selected are staff?

Accepted Answer

$$P(	ext{both staff}) = \frac{7}{10} 	imes \frac{6}{9} = 0.467$$

Question 6

Which formula correctly expresses the addition rule for two events A and B?

Accepted Answer

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

Question 7

A retail clothing store has 6 pairs of style A boots, 12 pairs of style B, and 2 pairs of style C. If a clerk randomly picks one pair, what is the probability it is style A or style C?

Accepted Answer

$$P(A 	ext{ or } C) = \frac{6+2}{20} = 0.4$$

Question 8

If the probability of a company earning a profit is 0.50, breaking even is 0.30, and losing money is 0.20, what is the probability the company does NOT earn a profit?

Accepted Answer

$$P(	ext{not profit}) = 1 - 0.50 = 0.50$$

Question 9

A small city has three airlines: 60% fly United, 30% Delta, and 10% Southwest. 70% of fliers are for pleasure, 30% for business. If airline and trip type are independent, what is the probability a flier uses Delta and is a business traveler?

Accepted Answer

$$P(	ext{Delta and Business}) = 0.30 	imes 0.30 = 0.09$$

Question 10

A golfer has 12 shirts (9 white, 3 blue). He selects one at random each day for two days, without replacement. What is the probability both shirts selected are white?

Accepted Answer

$$P(	ext{both white}) = \frac{9}{12} 	imes \frac{8}{11} = 0.545$$

Question 11

Which of the following is the correct formula for conditional probability?

Accepted Answer

$$P(E_1$|E_2$) = \frac{P(E_1$ 	ext{ and } E_2$)}{P(E_2$)}$$

Question 12

A Venn diagram shows $$P(	ext{Disney}) = 0.60$$, $$P(	ext{Busch}) = 0.50$$, $$P(	ext{Disney and Busch}) = 0.30. $$What is the probability a tourist visited either Disney World or Busch Gardens?

Accepted Answer

$$P(	ext{Disney or Busch}) = 0.60 + 0.50 - 0.30 = 0.80$$

Question 13

A drilling company estimates a 40% chance of striking oil. 60% of successful wells have a positive test, and 20% of unsuccessful wells have a positive test. If a well has a positive test, what is the probability it will be successful? (Use Bayes’ Theorem)

Accepted Answer

$$P(	ext{Success} | 	ext{Positive}) = \frac{0.4 	imes 0.6}{0.4 	imes 0.6 + 0.6 	imes 0.2} = \frac{0.24}{0.36} = 0.67$$

Question 14

Which of the following is NOT a requirement for a probability distribution?

Accepted Answer

The sum of all probabilities must be greater than 1.

Question 15

A jury member estimates the probability that a defendant is at fault as 0.30 after considering all evidence. What type of probability assessment is this?

Accepted Answer

Subjective probability assessment

Question 16

If $$P(A) = 0.7$$ and $$P(B) = 0.5$$, and $$A$$ and $$B$$ are independent, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$P(A 	ext{ and } B) = 0.7 	imes 0.5 = 0.35$$

Question 17

A table shows the probability distribution for the number of products sold: $$P(0) = 0.2$$, $$P(1) = 0.3$$, $$P(2) = 0.4$$, $$P(3) = 0.1. $$What is the probability that at least one product is sold?

Accepted Answer

$$P(	ext{at least one}) = 1 - P(0) = 1 - 0.2 = 0.8$$

Chapter 4: Introduction to Probability – Study Notes for Business Statistics

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