Week 3 Discussion

1. Discuss what is meant by classical probability assessment and indicate why classical assessment is not often used in business applications.

The classical probability assessment method is one in which we define an experiment and an event of interest. Then, we find out the total number of possible outcomes of the experiment where each outcome should be equally likely. We also find the total number of outcomes favorable to the event.

Let E be the experiment and A be the event of Interest.

Then by classical assessment method:

The classical definition is not often used in business application because this method demands that all outcomes of an experiment should be equally likely, which is not the case in real-life business. If this was so, then every business would either succeed or fail, the probability of each being 0.5.

This is not the case in real life and hence classical definition is not a good approach for business purposes.

2. Discuss what is meant by the relative frequency assessment approach to probability assessment.

The relative frequency approach assesses the probability of the real outcomes that have happened in the past. So, if the event of Interest is E, then by the relative frequency approach,

Suppose, the meteorological department wants to find out the probability that the annual rainfall in a particular region is more than 150mm.

The department also has past 25 years data of annual rainfall. Suppose out of the past 25 years, 15 years have received annual rainfall more than 150mm.

Then, probability that next year annual rainfall will be more than 150mm = 15/25.

3. Discuss what is meant by subjective probability. Provide a business-related example in which subjective probability assessment would likely be used.

Subjective probability is a type of probability derived from an individual’s personal judgment or own experience about whether a specific outcome is likely to occur. It contains no formal calculations and only reflects the subject’s opinions and past experience. Subjective probability can be contrasted with objective probability, which is the computed probability that an event will occur based on an analysis in which each measure is based on a recorded observation or a long history of collected data.

Being subjective when calculating probabilities is a way of quantifying the unknown and is a necessary part of life. Let’s say that you’ve been to your dentist twice and have spent $125 and $150 each time. You hear through the grapevine that the dentist has upgraded his office and that his fees have “skyrocketed.” You have two choices:

Guesstimate (i.e. use subjective probability) that you budget $300 to cover the potential bill.

Go to the dentist with no idea what the cost is going to be, receive a bill for $375, and completely destroy your budget.

4. Examine the relationship between independent, dependent, and mutually exclusive events.

A. Given that two events A and B are mutually exclusive, and that P (A) (≠) 0.

P (A|B) = 0, since if B has occurred, A can never occur.

B. If A and B are to be independent, then,

The LHS should be zero but it is given that RHS P (A) (≠) 0. Thus, since LHS ≠ RHS.

We can conclude that mutually exclusive events are not independent.

C.

(a) Since P(C/D) = 0.15 and not zero, the events are not mutually exclusive.

(b) Since two probabilities are not equal, i.e. P(C) not = P(C/D), the events are dependent.

(c) Are dependent events necessarily mutually exclusive events? No.