Problem Statement:
Process:Describe what you did in attempting to solve the problem. Do this part even if you did not solve the problem.
We drew a spinner then tested our theory that Beatrice would win more money. We spun 25 times and recorded who won each round. It turned out our guess was wrong.
Solution:State the solution clearly as you can. Explain how you know your answer is correct.
Al, even though he had less of a chance of winning each round, in the long run won more money because he had a weighted probability ratio that outnumbered Beatrices win-to-payout ratio.
Connection:What is the relationship between Expected Value, Observed Weighted Probability, & Theoretical Weighted Probability?
All of these are steps that work together to be able to create a bigger picture.
What are some real-life examples in which these
concepts are being used?
Evaluation: Discuss your personal reaction to the problem.
What did you learn from it? Win-to-pay can be better in the long run
Describe one Habit of a Mathematician that you used? I tested my theories.
How would you change the problem to make it better? I wouldn't change it actually. I think the assignment worked well in helping me to understand the concepts being taught.
Did you enjoy working on it? Somewhat, the hands on work helped me to understand the assignment.
Was it too hard or too easy? I personally thought that the assignment was neither too easy nor too hard. I think that it was a good assignment. I think that I learned a lot through it that I didn't know before this.
- Al and Betty decide to play a spinner game with toe spinner divided into two separate pieces. One fifth of the spinner is Al’s and four fifths of the spinner is Betty’s. Each time the spinner lands on Al’s section he wins $1.25, each time the spinner lands on Betty’s section she wins 30 cents. What are Al and Betty’s expected value per spin? How can the game be changed so that both Al and Betty have equal chances?
- Archibald and Beatrice are playing a card game. After they each pick a card the card is placed back into the deck. It doesn’t matter who draws the card, all that matters is the card which is drawn. If the card drawn is a jack the beatrice pays Archibald 20 cents. If the card drawn is a heart the Archibald pays Beatrice 8 cents. If neither a jack or heart is pulled from the deck then Archibald and Beatrice each give a penny to charity. What is the expected value per draw for Archibald, Beatrice, and the charity?
Process:Describe what you did in attempting to solve the problem. Do this part even if you did not solve the problem.
We drew a spinner then tested our theory that Beatrice would win more money. We spun 25 times and recorded who won each round. It turned out our guess was wrong.
Solution:State the solution clearly as you can. Explain how you know your answer is correct.
Al, even though he had less of a chance of winning each round, in the long run won more money because he had a weighted probability ratio that outnumbered Beatrices win-to-payout ratio.
Connection:What is the relationship between Expected Value, Observed Weighted Probability, & Theoretical Weighted Probability?
All of these are steps that work together to be able to create a bigger picture.
What are some real-life examples in which these
concepts are being used?
- flipping coins
- slot machines
- science experiments
Evaluation: Discuss your personal reaction to the problem.
What did you learn from it? Win-to-pay can be better in the long run
Describe one Habit of a Mathematician that you used? I tested my theories.
How would you change the problem to make it better? I wouldn't change it actually. I think the assignment worked well in helping me to understand the concepts being taught.
Did you enjoy working on it? Somewhat, the hands on work helped me to understand the assignment.
Was it too hard or too easy? I personally thought that the assignment was neither too easy nor too hard. I think that it was a good assignment. I think that I learned a lot through it that I didn't know before this.