Three Coins

Here, I added yet another coin, flipped these three coins 100 times, and recorded the outcomes like the previous experiment. Microsoft Excel randomly chose 0 or 1 100 times for each of the three coins, where 0 is heads and 1 is tails. Once again, I took the sum of the three coins. The possible sums were as follows: 0 + 0 + 0 = 0 (all three coins were heads), 0 + 0 + 1(in no particular order) = 1 (two coins landed on heads and the other on tails), 0 + 1 + 1(in no particular order) = 2 (one coin landed on heads and the other two on tails), or 1 + 1 + 1 = 3 (all three coins landed on tails). Next, I took the frequency of the possible sums, and the spreadsheet clearly shows the outcomes of this (remembering that I have only shown the first few flips). Heads appeared on all three coins 12 out of 100 times (12%), heads appeared on two of the three coins 42 out of 100 times (42%), heads appeared on one of the three coins 38 out of 100 times (38%), and heads did not appear on any of the three coins 8 out of 100 times (8%).

Probability of Getting 0 Heads:

Empirical: .08

Theoretical: .125

Probability of Getting 1 Head:

Empirical: .38

Theoretical: .375

Probability of Getting 2 Heads:

Empirical: .42

Theoretical: .375

Probability of Getting 3 Heads:

Empirical: .12

Theoretical: .125


Let's look at another simulation of the same experiment:

Probability of Getting 0 Heads:

Empirical: .11

Theoretical: .125

Probability of Getting 1 Head:

Empirical: .33

Theoretical: .375

Probability of Getting 2 Heads:

Empirical: .42

Theoretical: .375

Probability of Getting 3 Heads:

Empirical: .14

Theoretical: .125


 

 

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See what happens with four coins