How to analyze discrete probability distributions

Competency

This competency will allow you to demonstrate your ability to analyze discrete probability distributions and expected value.

Instructions

You have recently applied for a risk analyst position at G & B Consulting and been invited in for an interview. A part of the requirements of the job is a thorough knowledge of probability and statistics. Some of your potential future coworkers are given the opportunity to interview you and wish to test your knowledge.

Part 1: The first of these potential coworkers is explaining to you the importance of knowing the regional business landscape in order to be best prepared when new potential clients and how many specialists in different areas should be on hand. She shows you a spreadsheet predicting potential client types with the following information:

Client Type

Probability

Corporate

.45

Small Business

.11

Legal

.09

Government

.29

Private

Is there any reason to believe this information is not accurate? Explain to your potential coworker in detail any observations you may have in regards to the information on the spreadsheet.

Part 2: The next potential coworker you meet is excited to show you a dice game he developed that he is hoping to sell to a local casino. This game involves using two 10-sided dice with faces numbered 1 through 10. He asks you to confirm some of the probabilities of different outcomes of the game and show how you arrived at your answers.

What is the probability of rolling a sum of 11 on the two dice?
What is the probability of rolling the two dice and getting at least one seven?
What is the probability of rolling the two dice and getting either an odd sum or a sum greater than 19?
What is the probability of rolling doubles twice in a row?
Part 3: After confirming those probabilities, he tells you that the game costs $1 to play and has the following payouts:

Roll

Winnings

Doubles

Sum of 11

Sum of 3, 4, 18, or 19

$.5

Other

From these payouts, he tells you that the game should be incredibly popular since it has an expected value of 55 cents for every dollar spent. Your potential coworker wants to know if you agree with this expected value, and asks that you explain your reasoning, including any calculations you made.

Compile your responses from all parts into a single Word document for submission. Be sure to include all relevant work, and fully typed explanations where they are asked for.

Solution Preview

Part 1.
Yes, there is a reason to believe that the information above is not accurate. The information is inaccurate because the summation of those probabilities is not equal to one. Summation of all the probabilities in a given sample space must equal to 1.

(418 words)