Saturday, November 26, 2011

Probability of a Coin Flip

The probability of a coin flip landing on one side is 50%. This of course assumes that the coin is fair and the probability of heads or tails is thus even. The probability of a coin landing on heads or tails twice in a row is 25%. The reason is that there are now four possible outcomes: heads, heads; tails, tails; heads, tails; tails, heads.

The probability of a coin landing on heads or tails three times in a row is only 12.5% or one in eight. The reason is that there are now eight possible outcomes. With one flip the probability of one outcome is 50%. With two it becomes 25% and with three 12.5%. With each additional flip, the percentage is halved.

With this knowledge I decided to flip a 100 won coin three times in a row and repeat this eight times. Since the probability of heads resulting three times in a row was only 12.5% or one out of eight, I thought that I might get three heads in a row once out of eight tries. Here are the results of my experiment:

1) heads, heads, tails
2) heads, tails, heads
3) tails, heads, tails
4) heads, heads, heads
5) tails, heads, tails
6) heads, heads, tails
7) heads, heads, tails
8) tails, tails, tails

From my eight series of flips, I got three heads in a row once. I also got three tails once in a row. However, I got heads thirteen times and tails eleven times. This was not an even split. Instead of 50% heads and 50% tails, the result was 54% heads and 46% tails. Nevertheless, this was close to 50-50.

Based on this simple experiment, it may be that results are often close or identical to theoretical probability. I got three heads in a row once out of eight times which was exactly as predicted. I also got tails once out of eight as predicted. I did not get an even number of heads and tails but the results were very close to theoretical probability.

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