Purpose

To assess your ability to:

- apply probability concepts to business situation

- describe how various discrete probability distributions can be applied to solve business issues

- distinguish between classical, relative frequency and subjective approaches to probability

- identify the experiment, sample space, outcome and event in a situation

- compute probabilities of simple events

- apply probability concepts to business situation

- apply probability concepts to a business research project

Overview

This is a project in three parts:

1. Part One is subjective probability;
2. Part Two is a relative frequency probability; and
3. Part Three is classical or theoretical probability and compares the results of the three types of probability.

Project II, Part One: Subjective Probability

Before tossing the coins, make the following predictions. Remember the rule of a probability distribution is that the sum of all possible mutually exclusive outcomes has to be one (1). Note that getting 3 heads and getting exactly 5 heads are mutually exclusive events. Also, think about how the probability of getting 3 heads relates to the probability of getting 7 tails. Think about the situation and then answer the questions below with your best guesses. Do not look up or compute these probabilities but do think about the values. You will be graded on the reasonableness of your guesses. These are guesses, not computed values. Copy and paste this part into the rest of your project.

1. What percent of the time do you expect to get 5 heads?
2. What percent of the time do you expect to get 3 heads?
3. What percent of the time do you expect to get 7 heads?
4. What percent of the time do you expect to get no heads?
5. What percent of the time do you expect to get all heads?
6. Use your guesses above to fill in the chart below for all of the outcomes.
   
7. Adjust your guesses for 1-6 above until the two rules of probability are satisfied (Each value is between 0 and 1 and the sum of all of the probabilities is 1 .
8. After throwing 600 coins, how many heads would you expect?
9. How is the probability of getting three heads related to the probability of getting seven tails? Explain your answer.
10. How is the probability of getting three heads related to the probability of getting three tails? Explain your answer.

Project II, Part Two: Relative Frequency Probability

In this part of this project, you will determine probabilities through relative frequency.

1. You will be analyzing your results in an Excel spreadsheet, so create a spreadsheet with the following columns (you may abbreviate them if you like):

1. Toss Number (number your tosses from one (1) to 60 in this column.)
2. Number of Heads (See step 2 below)
3. Cumulative Number of Heads (See step 3 below)
4. Total Number of Coins Tossed so far(Number from 10 to 600 in increments of 10 )
5. Cumulative Percent Heads (See step 4 below)
6. Leave this column blank
7. Number of Successes (Number this column from 0 to 10 )
8. Subjective probability of Success (put your guesses from the chart in Part One)
9. Actual Successes (These values are the counts of how many times you got \(0,1,2, \ldots 10\) heads). You may use the Excel "countif' function to count your results.
10. Empirical Probability of Success (Column I divided by 60 )

\(K\). Theoretical probability of success (See Part 3 below)

2. Toss the ten coins 60 times, each time recording the Record the number of heads for each throw in the "Number of Heads" column.

3. Set up Excel to compute the cumulative number of heads (Column C). Use this column to have Excel compute the total number of heads that you have thrown so far. For example, if by the \(15^{\text {th }}\) throw you have gotten 60 heads total, then this column would read 60 . If on the \(16^{\text {th }}\) throw you got 8 more heads the cumulative column would read 68 for the \(16^{\text {th }}\) throw. You can use cell referencing to do this.).

4. Set up Excel to compute the Cumulative Percent of Heads (Column E) by dividing each cell in the Cumulative Number of Heads column by the number in the Total Number of Coins Tossed cell. Format this column to show four decimal places.

5. Use Excel to create a line graph of the Cumulative Percent of Heads that uses the Toss Number as the X-axis. Format the \(Y\) -Axis to go from 0.400 to 0.600.

Price: $16.1

Solution: The downloadable solution consists of 7 pages, 910 words and 3 charts.
Deliverable: Word Document