Investigating the Flip of a Coin Opens the Door to Math Education

Exactly how reliable and fair is the coin toss? For a coin toss to be completely fair, a coin needs to be perfectly constructed. Be a math citizen scientist, and join the project in figuring out the coin toss!

Flipping a coin is perhaps the most bias-free means of problem solving known to man. The simple choose-a-side-and-flip procedure leaves decision making entirely up to fate, providing quick solutions without debate. And it’s perfectly fair. Or is it?

According to statistics, coins should fall equally on their head or their tail. Scientifically speaking, a coin could technically also land on its grooved edge, but this is exponentially less likely to occur. Mathematically speaking, the occurrences of heads landings are essentially equal to the occurrences of tails landings that take place when a coin is flipped many times in a row. In order for this to be true, a flip must truly provide circumstances under which a coin is equally as likely to land on one side as it is to land on the other. In short: a coin’s weight distribution must be such that it isn’t slightly more likely to lean towards one side over the other. 

Coins have, historically, been truly even enough for us to consider them to be fair when flipped. However, scientists and statisticians began to wonder recently if the United States’ state-themed quarters might be less reliable due to the variation in designs and, as a result, the very slight differences in weight between coins and/or the subtle aerodynamic difference caused by differing coin patterns. So how can we be sure that the interesting and intricately decorated quarters made throughout the past decade and a half are still reliable? By participating in a citizen science project, of course!

Families can participate in Physics Central’s Physics Buzz Blog citizen science project by conducting some simple research at home. Using an online form, families can test state-themed quarters at home and then submit their heads-or-tails (or edge) landing data to the project, allowing scientists an ever growing bank of data on coin flipping. Not only is participation in the project a great way to support development of hand-eye coordination, but it will give children practice in conducting scientifically sound experiments and recording accurate and useful data.

Families who conduct their own experiments will need to spend some time examining the role of probability and ratios in their research. While it’s possible to participate without a mathematical understanding of these concepts, knowing why probability matters will help to add context to the experiment.

Additionally, participation in the project can support studies of United States history, climate, culture, and geography as well. While you flip state coins, consider the reasons for the design on each one. What role do geography, climate, history, and local culture play in each image? What can be learned about a state by looking at its themed quarter? Close examination of each design can spark further investigation into the story behind it.

[Photo credit: (cc) Nicu Buculei]