Fair Coin Experiment

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Instructions

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The following table shows the outcome recorded from flipping a fair coin 40 times

Trial numberstart upoutcomeTotal number of heads% heads1HT002TT003HT004TH1255HH2406TT233.337HH342.868TT337.59HH444.4410TH55011HH654.5512TH758.3313HH861.5414TT857.1415HT853.3316TH956.2517HT952.9418TT95019HH1052.6320TH115521HH1257.1422TH1359.0923HT1356.5224TT1354.1725HH145626TT1453.8527HT1451.8528TH1553.5729HH1655.1730TT1653.3331HH1754.8432TH1856.2533HT1854.5534TT1852.9435HH1954.2936TH2055.5637HH2156.7639TH2256.4139HH2358.9740TT2357.5 |
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A fair coin is an idealized randomizing device with two states, head and tail, which are equally likely to occur. The practical problem of checking whether a coin is fair is considered as easily solved by performing a sufficiently large number of trials, for this case 40 (Papoulis & Pillai, 2002).

The mean percentage of heads for each trial in the experiment is 48.34 as shown in the table below. This figure is approximately average. We can therefore say the probability of the coin falling on either side when flipped is almost 50%. Hence, the coin has been experimentally proven to be fair (Papoulis & Pillai, 2002).

N | Valid | 40 |
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Missing | 0 | |

48.3400 |

Below is a graph of percentage of heads against trial number. The graph shows an approximately normal behavior. It’s clear that what is seen in the graph align with what is in the table of experiment outcomes. Coin flipping is a simple and unbiased way of settling a dispute or deciding between two or more arbitrary options (Papoulis & Pillai, 2002). It is widely used in sports to decide arbitrary factors such as which side of the field a team will play from, or which team gets first use of the ball in football matches. Such decisions may tend to favor one side or maybe neutral. Flipping a coin helps make such decision without anyone of the teams complaining since flipping a coin is statistically proven to be fair.

Reference

Papoulis, A., & Pillai, S. U. (2002). *Probability, random variables, and stochastic processes*. Tata McGraw-Hill Education.