Question 1

If the probability of one event occurring is .40 and the probability of a second event occurring is 0.60, then the probability that both events will occur must be 1.0 since that is the maximum value a probability can be.

Accepted Answer

The probability of both events occurring is the product of their individual probabilities if the events are independent, which would be 0.40 * 0.60 = 0.24, not 1.0.

Question 2

If a company has the opportunity to bid on three contracts, A, B, and C, then the number of these contracts that are awarded to the company would be considered an elementary event.

Accepted Answer

An elementary event is an outcome of an experiment that cannot be further decomposed into simpler outcomes. In this case, the number of contracts awarded to the company is an elementary event because it cannot be further decomposed into simpler outcomes.

Question 3

If two events are mutually exclusive, it is possible for them to also be independent of each other.

Accepted Answer

Mutually exclusive events cannot occur at the same time, and if one event occurs, it completely rules out the possibility of the other occurring. This dependency between their outcomes means they cannot be independent. Independence implies that the occurrence of one event does not affect the probability of the other event occurring, which is not the case with mutually exclusive events.

Question 4

One of the difficulties in using the relative frequency of occurrence method for assessing probabilities in business situations is getting a large enough set of examples that match the one in question.

Accepted Answer

The relative frequency method requires a large number of observations to accurately estimate probabilities, and in many business situations, obtaining a sufficiently large and relevant dataset can be challenging.

Question 5

At a potato processing plant in the state of Washington, 400 potatoes have been examined for disease. Of these, four were diseased. Based on this, the plant manager has stated that the probability of finding a diseased potato is 0.01. He is applying subjective probability to arrive at this 0.01 value.

Accepted Answer

The plant manager is using empirical probability, which is based on the actual results of an experiment (in this case, examining 400 potatoes and finding 4 diseased ones), to calculate the probability as 4/400 or 0.01. This is not subjective probability, which would be based on personal judgment or belief rather than on specific numerical data.

Question 6

In playing the game Monopoly, the probability of a player landing on Park Place would be assessed using classical probability assessment.

Accepted Answer

In Monopoly, the probability of landing on any given space, including Park Place, can be calculated using classical probability because the game follows a set of defined, deterministic rules, such as the roll of dice to determine movement, making it possible to calculate the likelihood of landing on Park Place based on these known outcomes and the structure of the game board.

Question 7

A manufacturing company makes three types of products. Each time it makes a product, the item can be either good or defective and it can be either customized or standard. The events consisting of customized and defective would be considered mutually exclusive since they apply to different attributes of the product.

Accepted Answer

The events consisting of customized and defective are not mutually exclusive because a product can be both customized and defective at the same time; these attributes are independent of each other.

Question 8

A product that is produced at Ramsey Manufacturing goes through three steps to be built. At step one, the components are assembled by technicians. At step two, the product is sanded, and at step three the product is painted. The product can become defective if any of these three steps is performed incorrectly. The three steps are done by different people in different locations. We let D1 = defect introduced at step 1, D2 = defect introduced at step 2, and D3 = defect introduced at step three. Based on this situation these three events would be considered to be mutually exclusive.

Accepted Answer

The events D1, D2, and D3 are not mutually exclusive because a product can have defects introduced at more than one step in the process. For example, a product could have defects from both step 1 and step 2.

Question 9

Suppose a single die (a 6-sided cube with sides numbered 1 through 6) is rolled once. The event of interest is defined as rolling an even number. This can be said to be an elementary event.

Accepted Answer

An elementary event is an event that cannot be broken down into simpler events within the sample space. Rolling an even number (2, 4, or 6) consists of multiple outcomes, so it is not an elementary event; it is a compound event.

Question 10

A car salesman has noted that the probability that the dealership sells a car on a Saturday morning is .30. Then the probability of the dealership not selling a car on Saturday morning is .70.

Accepted Answer

The probability of an event not happening is 1 minus the probability of the event happening. So, 1 - 0.30 = 0.70.

Question 11

If you were planning to take a small group out to dinner on a Thursday evening and you were considering whether to call ahead for a reservation, the method of probability assessment you would most likely use to assess the chances of being able to get in for dinner without having a reservation would be subjective assessment.

Accepted Answer

Subjective assessment involves using personal judgment and experience to estimate the likelihood of an event, such as estimating the chances of getting a table without a reservation based on factors like the day of the week, the popularity of the restaurant, and past experiences.

Question 12

If a manager were interested in assessing the probability that a new product will be successful in a New Jersey market area, she would most likely use relative frequency of occurrence as the method for assessing the probability.

Accepted Answer

Relative frequency of occurrence is based on historical data of similar events, but for a new product with no past data, subjective probability or market research would be more appropriate.

Question 13

Suppose a coin is flipped twice. The event of getting heads on the first toss and the event of getting heads on the second toss could be said to be mutually exclusive.

Accepted Answer

Mutually exclusive events cannot happen at the same time. Getting heads on the first toss and getting heads on the second toss are independent events, not mutually exclusive, as one event does not affect the outcome of the other.

Question 14

Suppose a player is dealt 2 cards from a standard deck of 52 playing cards. To determine the probability of having a blackjack would involve classical probability.

Accepted Answer

Classical probability is used when all outcomes are equally likely, such as calculating the likelihood of specific hands in a card game from a well-shuffled deck. Calculating the probability of getting a blackjack (an ace and a 10-value card) from the first two cards dealt from a standard deck is a classic example of using classical probability.

Question 15

A car salesman states that the probability that the dealership sells a car on a Saturday morning is .30. The method of probability assessment that he has used is most likely classical assessment.

Accepted Answer

The method used is most likely empirical (or statistical) probability assessment, as it is based on past data or experience (e.g., historical sales data on Saturday mornings) rather than theoretical outcomes.

Question 16

The owners of Greg's Department Store have reason to believe that one of their employees has been stealing from the store. In an interview with the police, the owner says that she is 75 percent sure that the employee is stealing. This probability is an example of one that was assessed using classical probability.

Accepted Answer

The probability mentioned is an example of subjective probability because it is based on the owner's personal judgment and belief, not on a mathematical or statistical analysis of outcomes.

Question 17

Classical probability assessment is likely to be the most common method of probability assessment used in business decision making.

Accepted Answer

Classical probability assessment is based on equally likely outcomes and is not commonly used in business, where empirical or subjective probability assessments are more prevalent due to the complexity and variability of real-world situations.

Question 18

In most situations, there is no difference between the events and the elementary events.

Accepted Answer

Elementary events are the most basic outcomes that cannot be broken down further, whereas events can consist of one or more elementary events.

Question 19

When a patient arrives at a clinic complaining of several specific symptoms, the doctor who makes the diagnosis says that he is 80 percent certain that the patient has a particular problem. It is likely that he is basing this assessment on relative frequency of occurrence.

Accepted Answer

Doctors often use the relative frequency of occurrence, which is based on how often certain symptoms lead to a specific diagnosis in past cases, to estimate the probability of a patient having a particular condition.

Question 20

Two football teams play in the Super Bowl. The event of team A winning and the event of team B winning can be said to be mutually exclusive.

Accepted Answer

If team A wins the Super Bowl, team B cannot win it, and vice versa, making the events mutually exclusive since both cannot occur simultaneously.

Quiz 4: Introduction to Probability