Question 1

Which of the following is NOT a feature of a probability distribution?

Accepted Answer

The total of the probabilities for all possible events listed in the distribution must always add up to 1. If the total varies, it is not a valid probability distribution.

Question 2

Which of the following statements is untrue regarding a probability distribution?

Accepted Answer

A probability distribution does not necessarily show the average outcome that is expected to occur. It shows the probabilities of all possible outcomes. However, one can use the probabilities to calculate expected values or expected outcomes.

Question 3

The decision rule under the maximin criterion is to:

Accepted Answer

The maximin criterion is about addressing the worst-case scenario. Therefore, the decision rule is to select the alternative that has the best outcome should the worst event occur. This ensures that the decision-maker is prepared for any adverse situation and has a plan in place to mitigate the potential losses.

Question 4

The maximum amount that is worth paying to obtain additional information consists of:

Accepted Answer

The maximum amount worth paying for additional information is the difference between the expected value if the information is acquired and the expected value without the information. This is because the additional information can help to increase the expected value of a decision or investment, and the amount worth paying for it should not exceed the potential increase in value. Option A is not complete as it only considers the expected price of information, without taking into account the potential benefits. Option C is also not complete as it only considers the most likely benefit, without taking into account the potential range of benefits. Option D is too high as it considers the highest benefit which may not be realistic or achievable.

Question 5

Which of the following assumptions apply when making decisions on the basis of expected values:

Accepted Answer

The assumption that decision making on the basis of expected values is based on is that the decision will be repeated many times. This allows for the calculation of an average outcome, which is the expected value. Option A is incorrect, as the assumption does not require the decision to be a 'one-off'. Option B is also incorrect, as while there must be multiple outcomes, the assumption does not require there to be many possible outcomes.

Question 6

The following represent a tutor's estimate of the probability of students A, B, C and D failing an examination. Which student does the tutor consider has the best chance of passing the examination?

Accepted Answer

Student A has a probability of 0 of failing the examination, meaning they have the highest probability of passing compared to the other students.

Question 7

The most likely outcome represents:

Accepted Answer

The most likely outcome is the one with the highest probability of occurring, not necessarily the average or expected value.

Question 8

Which of the following is NOT a measure of uncertainty?

Accepted Answer

The expected value is not a measure of uncertainty, but rather a measure of central tendency. The other three choices (A, B, and D) are all measures of uncertainty.

Question 9

In a decision tree the boxes refer to:

Accepted Answer

In a decision tree, the boxes (often referred to as decision nodes) represent the points at which decisions have to be taken, indicating the different choices available at that juncture.

Question 10

The expected value represents:

Accepted Answer

The expected value is the sum of each possible outcome multiplied by its probability, which results in a weighted average of the possible outcomes.

Question 11

The joint probability of two events occurring together is:

Accepted Answer

The joint probability of two events occurring together is calculated by multiplying the probability of one event by the probability of the other event. This is because the probability of both events occurring simultaneously is equal to the probability of the first event occurring multiplied by the probability of the second event occurring, given that the first event has occurred.

Question 12

Which of the following represent states of nature?

Accepted Answer

States of nature refer to different conditions or events that may occur in the future, such as economic conditions like recession or boom. Options A and C refer to outcomes or courses of action, not states of nature. Option B refers to the most likely outcome, which is not the same as a state of nature.

Question 13

The following represent the expected values and standard deviations for alternatives a-d. Which alternative has the highest absolute risk?

Accepted Answer

Alternative B has the highest standard deviation (£75,000), which indicates the highest absolute risk among the options provided.

Question 14

Under what circumstances can risk reduction NOT be achieved from combining investments?

Accepted Answer

If the projects are perfectly positively correlated, it means that they move in the same direction and are affected by the same economic factors. Combining these investments will not result in risk reduction as there is no diversification benefit. In fact, combining such investments may increase the level of risk.

Question 15

Which of the following best describes objective probabilities?

Accepted Answer

Objective probabilities are derived from actual observed data from repeated experiments that simulate the decision under consideration. This means that choice A, repeating an experiment that exactly simulates the decision and using the data to derive the probability, is the best description of objective probabilities. The other options, obtaining an estimate from an expert or using a firm of management consultants, are based on subjective judgments and therefore not objective probabilities.

Quiz 12: Decision-Making Under Conditions of Risk and Uncertainty