We’ve all tried our luck. We have all been in situations where our desired outcome (success!) is not certain but instead depends on seemingly random events or other things outside of our control. A coin toss to determine who goes first is a very common example, and most people know the “odds” of winning a (fair) coin toss are 50-50. Often, determining the odds of an outcome (or the probability of outcome occurring) is more complicated and can depend on many factors, such as predicting the probability of rain. Moreover, sometimes the probability of an event occurring is counter-intuitive: it can be more or less likely than we might imagine.

Historically, the mathematical analysis of probability began with Gerolamo Cardano, Pierre de Fermat and Blaise Pascal in the mid 1600’s (towards the end of the Renaissance), and primarily focused on games of chance (such as games involving the throwing of dice). In the 1900’s probability analysis moved from games of chance to scientific applications, such as risk management (setting life insurance premiums), biology (probability of being born male or female) and physics (electron orbits around a nucleus).

Today, probability continues to play an important role in many businesses and industries. Many businesses continue to use probability to evaluate risk, which is critical to the decision-making process. In engineering, reliability analysis (estimating the amount of time before a system will fail) is based on probabilities and is an important step in the design of many types of systems (including transportation and communication). And important statistical methods, such as hypothesis testing, are also based on probabilities.

In this project, students will connect with their studies of the Renaissance era and use their creativity and building skills by to reproduce (and possibly adapt) a Renaissance-era game that involves some type of “chance”. A challenging component of this project is the requirement for students to model real-life mathematicians and apply their acquired understanding of probability theory and analyze the probabilities associated with that game to better understand the odds of winning (or the probability of other game-specific events occurring).