Influencing a Coin Toss
A basic science fair project involving coin tosses tries to determine whether a person can influence the outcome of a coin toss by manipulating certain factors. The experiment involves tossing a coin 100 times and letting it land naturally. After recording these results, the same coin is tossed 100 times and the tosser tries to get it to land on a table heads up. Then the same coin is tossed another 100 times, only this time the tosser is told to catch the coin in mid-air, slap it onto the back of his hand and try to make it come up heads. Catching the coin emerges as the method that made the coin come up heads most often.
Fair Coin Toss
This project involves two people tossing coins at the same time. Each person is assigned one of two "winning" results. One person gets a point if both coins match, i.e., two heads or two tails, and the other gets a point if he lands one heads and one tails. Both participants are asked if one has a better chance of winning than the other. This experiment reveals a bias in human nature, as the person on the matching coins side appears to have an edge, as he seems to have two outcomes to the other person's one. In reality, both have an equal chance.
Landing a Coin on its Side
This science fair project idea comes from examining the physics of a coin toss. The odds of one coin being tossed and landing straight up on its edge are very slim, but the odds of a roll of coins landing on edge are quite high. The student begins the experiment by tossing one coin to see if it lands standing on edge. The student then glues another coin to the first and tosses it again. He keeps adding coins until discovering how fat a coin needs to be to land on its edge.
The Digital Coin
A more advanced science fair project involves writing a computer program to simulate the results of a coin toss. The student designs a Python program that allows users to calculate the results for X number of coin tosses. This project showcases the laws of probability and also the usefulness of computer science in mathematics. As a science fair project, students could set up a computer and let participants run the program themselves.