For this investigation, I used Microsoft Excel to "flip" my coins. I let Excel randomly select 0 or 1 100 times for each of my five experiments (using one coin, two coins, three coins, four coins, and five coins). I let 0 stand for heads and 1 stand for tails. With the exception of the first experiment with one coin, I used the sum of the outcomes to find the frequency of how many times heads appeared within the given experiment. Since I used 0 and 1, the sum tells exactly how many heads or tails appeared in each flip. For instance, if the sum was 2 and I was testing four coins, I knew that there had to be two heads and two tails. The graphs for each experiment show the frequency of heads appearing. The 2 tables below sum up the graphs. The final table is for comparison to the theoretical probabilities.
 
1st Simulation:

	Percent of 0 Heads	Percent of 1 Head	Percent of 2 Heads	Percent of 3 Heads	Percent of 4 Heads	Percent of 5 Heads
One Coin	.50	.50
Two Coins	.24	.50	.26
Three Coins	.08	.38	.42	.12
Four Coins	.05	.18	.40	.31	.06
Five Coins	.02	.13	.27	.35	.20	.03

 

 

---

2nd Simulation:

	Percent of 0 Heads	Percent of 1 Head	Percent of 2 Heads	Percent of 3 Heads	Percent of 4 Heads	Percent of 5 Heads
One Coin	.47	.53
Two Coins	.31	.47	.22
Three Coins	.11	.33	.42	.14
Four Coins	.02	.23	.43	.30	.02
Five Coins	.02	.14	.41	.33	.09	.01

 

---

Theoretical:

	Percent of 0 Heads	Percent of 1 Head	Percent of 2 Heads	Percent of 3 Heads	Percent of 4 Heads	Percent of 5 Heads
One Coin	.50	.50
Two Coins	.25	.50	.25
Three Coins	.125	.375	.375	.125
Four Coins	.0625	.25	.375	.25	.0625
Five Coins	.03125	.15625	.3125	.3125	.15625	.03125

 

---

 

Back to title page