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# Probability Project – Fair Coin, Essay Example

Pages: 3

Words: 926

Essay

Procedure

A fair coin was flipped 25 times and the outcomes were recorded. All coins were flipped starting with heads facing upwards, and were then flicked into the air and caught. The side of the coin that was facing upwards as the coin was caught was recorded as the side that the coin landed on. When the coin was dropped, it would not count and the coin would be flipped once more; the results only count if the coin was successfully caught. The data was recorded in a manner that accounts for the side of the coin that the coin started on before it was flipped and whether heads or tails was retrieved. At the end of the study, the total number heads and the percentage of heads was calculated.

Results

Table 1: The total amount of heads received in terms of number and percentage

 Trial Number Start Up – H or T Outcome H or T Total Number of Heads % Heads 1 H H 1 100 2 H T 1 50 3 H T 1 33.3 4 H T 1 25 5 H T 1 20 6 H H 2 33.3 7 H H 3 42.9 8 H T 3 37.5 9 H T 3 33.3 10 H H 4 40 11 H T 4 36.4 12 H T 4 33.3 13 H H 5 38.5 14 H H 6 42.9 15 H T 6 40 16 H T 6 37.5 17 H T 6 35.3 18 H T 6 33.3 19 H H 7 36.8 20 H H 8 40 21 H H 9 42.9 22 H T 9 40.9 23 H H 10 43.5 24 H T 10 41.7 25 H T 10 40 Total 10 40%

Discussion

The percent heads column is 40%, which deviates from the expected value of 50%. However, this is likely the case because only 25 coin tosses were used. The sample began with 100% heads, and this number slowly fluctuated to values that were close to 40%. If more coin toss trials are conducted, it is likely that the percentage of coin tosses will approach 50% because random chance becomes a minimized factor as the sample size grows larger (Larson & Farber, 2001).

Table 2: Trial number versus the percentage of heads.

 1 x .9 .8 .7 .6 .5 x .4 x x x x x x x x x x x x x x x x .3 x x x x x x .2 x .1 0 X   y 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

As shown in table 2, the number of the trial correlates to the percentage of heads observed. In the table, all percentage values are converted to a decimal and rounded to the nearest tenth. At first, the values deviated from the expected 50%, but this effect became normalized after the third coin toss, which agrees with the results presented in table 1. Furthermore, starting with the 6th coin toss, all values were found to be rounded to either .3 or .4, indicating that the probability function is beginning to reach the expected 50%. It is likely that is 100 tosses were conducted, the numbers would begin to fluctuate between .4 and .5, before finally demonstrating that .5 is the most common probability for heads.

This probability indicates that coin tosses aren’t completely reliable as a 50% chance. In theory, the official coin flip at a sporting event should yield heads half of the time and tails the other half of the time. However, this probability deviates, providing one team a significant advantage over the other with regards to the coin toss. It appears that the probability of a coin is only accurate if it is flipped many times. Since it is flipped just once at the beginning of a sporting event, these conditions for fairness are not upheld.

References

Larson, R. and Farber, B. (2001). Elementary Statistics: Picturing the Word (5th ed.).Upper Saddle River, NJ: Pearson Prentice Hall.

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