Four Coins

My next experiment was to flip four coins, using Microsoft Excel to randomly select 0 or 1 100 times for four different coins, but I have only shown a few flips). I used the sum to find the frequency of how many times heads appeared. The possible sum outcomes were as follows: 0 + 0 + 0 + 0 = 0 (all coins landed on heads), 0 + 0 + 0 + 1(in no particular order) = 1 (three of the four coins landed on heads), 0 + 0 + 1 + 1 = 2 (two of the four coins landed on heads), 0 + 1 + 1 + 1(in no particular order) = 3 (one of the four coins landed on heads), or 1 + 1 + 1 + 1 = 1 (none of the four coins landed on heads). The spreadsheet shows the frequency of these possible outcomes: heads appeared on all four coins 6 out of 100 times (6%), heads appeared on three of the four coins 31 out of 100 times (31%), heads appeared on two of the four coins 40 out of 100 times (40%), heads appeared on one of the four coins 18 out of 100 times (18%), and heads did not appear at all 5 out of 100 times (5%).

 

Probability of Getting 0 Heads:

Empirical: .05

Theoretical: .0625

Probability of Getting 1 Head:

Empirical: .18

Theoretical: .25

Probability of Getting 2 Heads:

Empirical: .40

Theoretical: .375

Probability of Getting 3 Heads:

Empirical: .31

Theoretical: .25

Probability of Getting 4 Heads:

Empirical: .06

Theoretical: .0625

 

 


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

Probability of Getting 0 Heads:

Empirical: .02

Theoretical: .0625

Probability of Getting 1 Head:

Empirical: .23

Theoretical: .25

Probability of Getting 2 Heads:

Empirical: .43

Theoretical: .375

Probability of Getting 3 Heads:

Empirical: .30

Theoretical: .25

Probability of Getting 4 Heads:

Empirical: .02

Theoretical: .0625

 

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See what happens with five coins