Analyze Discrete Probability Distributions

ANALYZE DISCRETE PROBABILITY DISTRIBUTIONS

You have recently applied for an analyst position at G&B Consulting and have been invited in for an interview. A part of the interview requirements for the job is presenting a thorough knowledge of probability and statistics. Some of your future potential coworkers are given the opportunity to interview you and wish to test your knowledge.
The first interviewer you meet with is explaining to you the importance of knowing the regional business landscape in order to be best prepared for new potential clients. 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 interviewer why you feel this information is or is not accurate.
The next interviewer you meet with is excited to show you a dice game he has developed that he is hoping to sell to a local casino. The 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 getting at least one 7 when rolling the two dice?
What is the probability of getting either a sum less than 4 or a sum greater than 18?
What is the probability of rolling doubles twice in a row?
After confirming those probabilities, he tells you that the game costs $1 to play and has the following payouts:
ROLL WINNINGS
Doubles $4
Sum 11 $1
Sum 3, 4, 18, 19 .50
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. Do you agree with this expected value? Explain why or why not?
Create a report using Microsoft Word that will detail your responses to the interviewers. Show all work, including any tables or formulas used, and any necessary explanations with your solutions.