question archive Module 3 Group Activity 2 Math 180 Part A – Designing Your Game (Individual) Suppose you want to design a simple game for a fundraiser for your local school district
Module 3 Group Activity 2 Math 180 Part A – Designing Your Game (Individual) Suppose you want to design a simple game for a fundraiser for your local school district
Subject:SociologyPrice: Bought3
Module 3 Group Activity 2
Math 180
Part A – Designing Your Game (Individual)
Suppose you want to design a simple game for a fundraiser for your local school district. The game requires a player to select five balls from an urn that contains 1000 red balls and 4000 green balls.
1. If a player selects a single ball from the urn, what is the probability of selecting a red ball?
2. Treat the probability from #1 as , the probability of success. Assume this probability is fixed for all trials of the experiment. Explain why this assumption is reasonable.
3. Build a probability model that describes the number of red balls selected, , in trials of the experiment. (You may add or remove rows as needed).
|
|
Probability |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
4. You decide to charge $20 to play the game. For each game played, you would like to make $5. Decide on payouts for 0, 1, 2, 3, 4, and 5 balls selected. Verify the expected value of the game is $5.
|
|
Payout |
|
0 |
|
|
1 |
|
|
2 |
|
|
3 |
|
|
4 |
|
|
5 |
|
5. Now, let’s play the game! Go to StatCrunch and select Applets > Simulation > Urn Sampling and conduct 1 Run (play one game). How many red balls were selected? Click 1 Run a second time. How many red balls were selected?
|
Run |
Red Balls |
|
1 |
|
|
2 |
|
6. Click 1000 Runs at least five times (to generate at least 5000 more results of the game). Create a frequency distribution of the number of red balls selected based on the results of the simulation.
Copy Graph
Part B – Analyzing Your Games (Group)
Work with your group to answer each of the following questions. Submit this entire worksheet to the appropriate discussion board in Blackboard.
7. Compare the relative frequencies from the simulation to the probability model built from the binomial probability distribution in #3. Do you believe the independence assumption was reasonable?
Type Answer
8. Compare your individual answers for #7 and decide on a payout structure as a group.
|
|
Payout |
|
0 |
|
|
1 |
|
|
2 |
|
|
3 |
|
|
4 |
|
|
5 |
|
9. Compute the mean winnings per game played based on the simulation and the payouts you decided on.
Type Answer
10. Assuming the mean earnings per game are the value found in #9. Suppose the game is played 1000 times at the fundraiser. How much money did the game raise for the school district?
Type Answer
11. Suppose the game is only played 100 times at your fundraiser. Explain the risks involved in making this game available.
Type Answer
This worksheet was adapted from content in the “Activity Workbook” Copyright © 2017 Pearson Education, Inc.
that accompanies the e-text Interactive Statistics, 2nd Edition by Sullivan and Woodbury
