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.