Create an Excel spreadsheet with columns for each step

Dominique785 

To create an Excel spreadsheet that calculates the Expected Monetary Value (EMV) of playing the Powerball, you will need to calculate the probabilities of all possible outcomes, the prize for each outcome, and the contribution of each outcome to the overall EMV. Here's how you can structure the spreadsheet and automate the calculations using Excel formulas:

1. Structure of the Spreadsheet

You will have the following columns in your spreadsheet:

• Outcome: Description of the possible outcome.
• Probability: Probability of each outcome.
• Prize: The prize for each outcome.
• EMV Contribution: The EMV contribution of each outcome, calculated by multiplying the probability by the prize.

Steps to Create the Spreadsheet:

A. Setting Up the Table:

B. Filling in Probabilities:

The probabilities for each outcome are based on the Powerball rules. Powerball involves picking 5 numbers from 1 to 69 and 1 Powerball number from 1 to 26. The probabilities are as follows:

• 5 Numbers + Powerball: 1292,201,338\frac{1}{292,201,338}292,201,3381​
• 5 Numbers: 111,688,054\frac{1}{11,688,054}11,688,0541​
• 4 Numbers + Powerball: 1913,129\frac{1}{913,129}913,1291​
• 4 Numbers: 136,525\frac{1}{36,525}36,5251​
• 3 Numbers + Powerball: 114,494\frac{1}{14,494}14,4941​
• 3 Numbers: 1579\frac{1}{579}5791​
• 2 Numbers + Powerball: 1701\frac{1}{701}7011​
• 1 Number + Powerball: 191\frac{1}{91}911​
• Powerball Only: 138\frac{1}{38}381​
• No Prize: Remaining Probability\text{Remaining Probability}Remaining Probability

You can input these probabilities directly into your Excel sheet.

C. Filling in Prizes:

The prizes for each outcome are as follows (standard Powerball payouts):

• 5 Numbers + Powerball: Jackpot (can be variable, but for the calculation use a hypothetical value, e.g., $100,000,000)
• 5 Numbers: $1,000,000
• 4 Numbers + Powerball: $50,000
• 4 Numbers: $100
• 3 Numbers + Powerball: $100
• 3 Numbers: $7
• 2 Numbers + Powerball: $7
• 1 Number + Powerball: $4
• Powerball Only: $4
• No Prize: $0

D. Calculating EMV Contribution:

For each outcome, the EMV Contribution is calculated as: EMV Contribution=Probability×Prize\text{EMV Contribution} = \text{Probability} \times \text{Prize}EMV Contribution=Probability×Prize

In Excel, you can use the following formula in the EMV Contribution column (for row 2, assuming row 2 contains the first outcome):

= B2 * C2

You can then drag this formula down for all the outcomes.

E. Calculating Total EMV:

The Total EMV is simply the sum of all the EMV contributions. You can calculate it using the following formula:

= SUM(D2:D10)

This value will give you the overall Expected Monetary Value for playing the Powerball.

2. Interpreting the Results:

After calculating the Total EMV, it is highly likely to be negative due to the extremely low probabilities of winning large prizes and the relatively low prizes for most outcomes. This negative EMV reflects the expected loss for each ticket bought.

3. Discussing the Results:

In your final report, you can discuss the implications of the negative EMV:

• Risk: Powerball has a very low probability of winning significant prizes, and the negative EMV means that, on average, players are expected to lose money over time.
• Popularity: Despite the negative EMV, Powerball remains popular due to the allure of the massive jackpots and the small cost of participation ($2 per ticket).
• Conclusion: While playing Powerball can be fun, it's important for players to recognize the low likelihood of winning large prizes and that, statistically, they will lose money in the long run.

Example of What the Sheet Will Look Like:

This table suggests that the overall EMV is negative, meaning that on average, every Powerball ticket bought results in a loss of $1.37 (assuming a ticket costs $2).

The text and the formulas was created with the help of AI.

My answers are voluntary and without guarantee!

Hope this will help you.

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