Checking the Fairness of a Coin





Checking the Fairness of a Coin


The report herein explores the possibility of whether a coin is fair or biased when tossed number of times. It involves an experiment that was carried out by tossing a coin for fifty times. The main objective for the activity was to get a definite answer that addresses the fairness or biasness of a coin. It was important to carry out the test to determine the number of times the coin would land on the head or on the tail. The results obtained from the experiment were analyzed and interpreted. A conclusion was then given that more studies need to be done to determine how fair or biased the coin is.


Numerous theories have been made in the intention of determining the fairness or biasness of a coin. Most believe in the null hypothesis, which concludes that the coin is fair and at times, it is biased. This observation raises the question of whether the coin is in deed fair or biased. It was therefore necessary to carry out a test that would satisfy the speculation. This was accomplished through an experiment whereby a coin was flipped fifty times to determine if it fell on the heads or tail. Through this experiment, the findings would address the question of whether there exists fairness of biasness in a coin. It was a significant test since at the end it gave a clear conclusive argument to the problem.

Literature Review

In order to end the speculation on the fairness of the coin, a hypothesis test is necessary. This is a way of analytically calculating how certain a statistical experiment is. Probability and statistics therefore are used to determine if chance alone is explanation enough for such outcomes.

According to Classics (1) probability is a mathematical theory that deals with patterns that occur in random events. It is also described as the calculation of the possibility of an event occurring. Probability is the demonstration of probabilistic perceptions in terms that are reflected on separately from their meaning. It is used on a daily basis mostly in assessing risks and in financial markets.

The assessments are widely used in the community to assist in contributing to decisions. In any decision that is made, there is a risk involved and thus the existence of a probability of whether it will work or not. The theory also applies heavily on reliability. Many companies use it calculate the chances of reducing failure in their products.             According to Wikipedia (1), probability in mathematics is widely used in trying out the production of results. It is a method of allocating a value of between zero and one to every event. The possibility of a coin, when flipped, is expected to have a fifty/fifty chance on falling on the tail or head.

Math is Fun (1) state that the probability of the coin landing on the head is a half but so is that of the same coin landing on the tail. Thus the likelihood of an event happening is equivalent to the number of ways it can happen divided by the number of total outcomes. The probability line is mostly used to show the chance of the event happening. The line starts from impossible, unlikely, even chance, likely and ends at certain. Therefore the chance of an event occurring is held in between impossible and certain or zero and one respectively (Math is Fun 1). This means that the possibility of an event cannot be less than zero or more than one.

Materials and Methods

I carried out an experiment in which I tossed a coin fifty times, to establish whether it falls on heads (H) or tails (T). The materials that I needed for the experiment were limited to a coin, a pen and paper for recording the data. I tossed the coin fifty consecutive times while pausing in between every toss to record whether the previous flip landed on a head or tail.


After the experiment, I gathered up the information collected and made a comprehensive report out of the findings. I counted the total number of heads and tails that I had recorded and listed them down on an excel sheet. Out of my fifty tosses, the coin fell on 23 heads and 27 tails.


After analysis of the results from the experiment, the expectations were not met as anticipated. The coin was flipped fifty times thus the expectation was 25 times each for both heads and tails to indicate a fifty/fifty chance. The outcome was however different in that it produced 23 heads and 27 tails. This however does not indicate that the coin is not fair. Prior studies indicate that if the experiment is conducted repeatedly, it will produce different results that will vary around a mean. It is important to consider the fact that probability is just a guide and does not fully indicate what will happen.


The margin of error between the expected 25 heads that turned out to be a 23 and 25 tails that came to 27 is expected when doing probability test. This should not be used as a determinant of the fairness and the biasness of a coin since different test will give different results. In my conclusion, these findings therefore do not actually qualify to declare the coin whether fair or biased. I therefore suggest that more study needs to be done in order to come up with more evidence to the question.

Works cited

Classics, Cosimo. “What is Probability?” Cut the Knot. 2007. Web. 31 Jan 2014.

Probability. Math is Fun. n.d. Web. Jan 31 2014.

Probability. Wikipedia. 16 Jan. 2014. Web. 31 Jan 2014.

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