Game r
- 1. Diamonds are everybody’s best friend! Team R
- 2. How it works The player will give the dealer $5 to play. The player will then randomly select a card from a deck of 52 cards. If the player picks a diamond, they will win $10. If they select a heart, they will receive $7, and if they pick either a club or a spade, they will receive no money. Afterwards, the selected card will be placed randomly back into the deck.
- 3. Expected Mean/Std. Dev. x +$5 (diamond) +$2 (heart) -$5 (club/spade) P(x) 0.25 0.25 0.5 Expected Mean: μx = (5 x 0.25) + (2 x 0.25) + (-5 x 0.5) μx = -$0.75 Expected Standard Deviation: σ²x = (5 + 0.75) ² 0.25 + (2 + 0.75) ² 0.25 + (-5 + 0.75) ² 0.5 σ²x = 19.19 σ = 4.38
- 4. The Procedure x +$5 (diamond) +$2 (heart) -$5 (club/spade) P(x) 0.2 0.28 0.52 Simulated Mean: μx = (5 x 0.2) + (2 x 0.28) + (-5 x 0.52) μx = -$1.04 Simulated Standard Deviation: σ²x = (5 + 1.04) ² 0.2 + (2 + 1.04) ² 0.28 + (-5 + 1.04) ² 0.52 σ²x = 18.0384 σ = 4.2472
- 5. Conclusion The values found through the simulation were extremely close to the predicted values. The simulated mean was slightly lower than the predicted mean, but only by 29 cents. Additionally, the standard deviations remained within 0.2 of each other; they were extremely close. To improve the game, I would shuffle the selected card back in rather than place it in randomly.