Game c
- 2. Description To play my game all you must do is flip a coin 3 times. It is $12 to play. The goal of the game is to flip as many heads as you can in your 3 tosses. For every heads you flip, you earn $10. For every tails you flip, you LOSS $2. In your 3 tosses if you flip 1 heads and 2 tails you would win $6 back.
- 3. Theoretical Data # of Heads 0 1 2 3 $X -6 6 18 30 P(X) .125 .125 .125 .125 -6(.125)+6(.125)+18(.125)+30(.125)=6 .125(-.75-6)^2+.125(.75-6)^2+.125(2.25-6)^2+.125(3.75-6)^2=11.54 Square Root(11.54)= 3.40 Expected Value= 6 Standard Deviation= 3.4
- 4. Experimental Data # of Heads Flipped 0 1 2 3 Frequency 4 25 17 4 # of Heads 0 1 2 3 $X -6 6 18 30 P(X) .08 .5 .34 .08 -6(.08)+6(.5)+18(.34)+30(.08)= 11.04 .08(-.48-11.04)^2+.5(3-11.04)^2+.34(6.12-11.04)^2+.08(2.4-11.04)^2= 57.14 Square Root(57.14)= 7.56 Expected Value= 11.04 Standard Deviation= 7.56 http://www.youtube.com/watch?v=ZRNt2YOzH08 –Video of my game
- 5. Conclusion The theoretical and experimental expected values were about $5 apart. I took in account the standard deviation of the theoretical data and made the cost to play the game just beyond that at $12. Since the expected value for the experiment was about $11, for every game played I would receive about $1 in profit. That is almost 10% profit with every game so I would say my game would be successful if people played it.