This competency will allow you to demonstrate your ability and skill in applying counting principles and analyzing binomial distributions.
You have just been hired by G & B Consulting and given your first assignment. A local independently wealthy citizen who enjoys gambling and baseball, but not math, has asked you to help him determine the likelihood of the Boston baseball team winning the upcoming playoff series against Cleveland’s baseball team. He will be traveling to Las Vegas shortly and is looking forward to placing some bets on the series.
During the regular season, the two teams played 7 times, and Boston won 5 of the games. For the playoffs, the first team to win 4 games wins the series. Use this information to determine the probability of a variety of outcomes.
Part 1: Your client wants to place a series of bets based on different ways Boston may end up winning the series and asks you to determine the following:
- Based on the regular season record, what would you expect the probability of Boston winning any single game?
- What is the probability of Boston winning the series in 4 games?
- What is the probability of Boston winning the series in exactly 5 games?
- What is the probability of Boston winning the series in at least 6 games?
- How would you describe to your client why separate calculations are needed for each scenario?
Part 2: Working in parallel, your coworker came up with the following results:
The probability of Boston winning in exactly 5 games is approximately 37.2%. Before you return to the client with your results you need to make sure that you are in agreement and can justify to all parties the validity of your work. Compose an email to your coworker with your conclusion about his work.
Part 3: Prepare a summary report for your client with the results you found in part 1. However, you also wish to caution your client that your work is purely mathematical, and there are and other factors can affect the outcome of these games. Identify at least two other factors that could influence the outcome and explain them to the client. Identify one other factor that specifically addresses why using a binomial distribution may not be appropriate here.
In a single document, compile all of your work from Parts 1, 2, and 3 for submission. Be sure to include all relevant work and clearly label each part.