Addmaths SBA
Project Title:
To investigate the fairness of a particular coin being used by a cricket umpire of ** ********* *****’ High School.
Purpose of Project:
Problem Statement: The Cricket Club of *** has been hosting a cricket competition over the past couple weeks. The Physical Education Captain of the school was delegated the position of umpire, and has therefore been making the coin toss at the start of each cricket match, using a special coin. However, many cricket captains have become suspicious of the said Physical Education Captain and have begun to question her integrity after failing to win a toss for several subsequent matches, with respective subsequent tosses. It is being thought that she is unfairly manipulating the tosses . This dilemma was reported to the Physical Education teacher of the school. It was decided that if the Physical Education Captain was indeed, proven guilty, she would be stripped of her reputable position, since such practices do not support good sportsmanship. With her integrity and position at stake, it is therefore necessary to carry out a series of similar coin tosses in order to determine whether or not the said Physical Education Captain is, in fact, unfairly manipulating the outcome. By the laws which govern classical probability, it can be said that the probability of a fair coin landing as heads or tails during a toss is 0.5. If a series of subsequent coin tosses are carried out and one outcome is being particularly favoured, therein lies the probability of the coin being fixed, or biased. This may be due to external factors, namely which hand was used to make the toss and which coin face was turned upwards. By means of a series of simple experiments using the same coin as the Physical Education Captain, I seek to determine whether or not varying factors of the manner of throwing the coin do, in fact, influence the outcome. This is given that the coin tosses are conducted in a non-uniform manner by the
To investigate the fairness of a particular coin being used by a cricket umpire of ** ********* *****’ High School.
Purpose of Project:
Problem Statement: The Cricket Club of *** has been hosting a cricket competition over the past couple weeks. The Physical Education Captain of the school was delegated the position of umpire, and has therefore been making the coin toss at the start of each cricket match, using a special coin. However, many cricket captains have become suspicious of the said Physical Education Captain and have begun to question her integrity after failing to win a toss for several subsequent matches, with respective subsequent tosses. It is being thought that she is unfairly manipulating the tosses . This dilemma was reported to the Physical Education teacher of the school. It was decided that if the Physical Education Captain was indeed, proven guilty, she would be stripped of her reputable position, since such practices do not support good sportsmanship. With her integrity and position at stake, it is therefore necessary to carry out a series of similar coin tosses in order to determine whether or not the said Physical Education Captain is, in fact, unfairly manipulating the outcome. By the laws which govern classical probability, it can be said that the probability of a fair coin landing as heads or tails during a toss is 0.5. If a series of subsequent coin tosses are carried out and one outcome is being particularly favoured, therein lies the probability of the coin being fixed, or biased. This may be due to external factors, namely which hand was used to make the toss and which coin face was turned upwards. By means of a series of simple experiments using the same coin as the Physical Education Captain, I seek to determine whether or not varying factors of the manner of throwing the coin do, in fact, influence the outcome. This is given that the coin tosses are conducted in a non-uniform manner by the