What is the probability of rolling a sum of 11 on the two dice?

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

.7

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

$4

Sum of 11

$1

Sum of 3, 4, 18, or 19

$.5

Other

$0

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.

REQUIREMENTS:
– The math calculations demonstrate correct mathematical thinking, and there are no or minor errors in the game. All work is shown.
– Communication about the problems was very constructive and professional. Each solution was fully presented. A thorough explanation for how to obtain each solution was stated.

– Thoroughly explains why the game is popular, and makes connection to expected value. Correct calculations included with minor errors.