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Probability Project Design Your Own Game. Jimanne Jackson's "Wonders of the wheel" Game
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Probability Project Design Your Own Game.
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By: Jimanne Jackson-Cox (dankkut) .
Game instructions
Jimanne Jackson's "Wonders of the Wheel" Game .
Begin by going to this website to roll virtual dice: https://freeonlinedice.com/
Then, click on this link to bring you to a virtual spinner website: http://www.shodor.org/interactivate/activities/AdjustableSpinner/
Set the sections of the spinner to the following measurements:
Blue- 12.5
Pink- 3.61
Gray- 21.39
Orange- 12.5
Green- 6.11
Red- 18.89
Purple- 12.5
White -12.5
Now, spin the spinner!
Game Rules
If you rolled a one on the die, and landed on the green section of the spinner, then congratulations because you win first place! The prize for first place is 500 Billz Bucks. If you did not win first place, do not worry, because there is a second place prize too! If you rolled a prime number on the die and landed on the green or pink section of the spinner then you win second place! Reminder, that the prime numbers on a die are 2, 3, and 5. The second place prize is 50 Billz Bucks.
Calculations
Theoretical Probability:
Expected Value:
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E(X) = (490 * 0.010183) + (40 * 0.0486) - (10 * 0.9412) = -$2.47833
Therefore, the expected value of our game is to lose $2.48 on average, so it is not a fair game as Loka has a higher probability of earning money.
Game Results
Experimental Probability
Comparison between experimental and theoretical probabilities
After making the theoretical probability distribution chart, it was clear that there were very slim chances of winning the first place prize, and only a slightly better chance of winning second place. The likelihood of winning first place was calculated to be 0.010183, and second place was 0.0486. This is very small compared to the probability of losing, which was 0.9412. The expected value was calculated to be a loss of $2.48 for the player, each time the game was played.
Once we played our game, we were surprised by how many second place prizes we won, since the calculated probability was so small. We were also surprised to win first place once. We expected there to be far more losses, especially since our expected value was calculated to be a loss of $2.48 each time we played. When we made the probability distribution table using the experimental values, we found that the probability of winning the first place prize and second place prize were both significantly higher than in our theoretical probability. Our expected value was what surprised us the most, as it stated that the player would win $11.00 on average each time the game was played.
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