Scratching the Surface of Probability

Scratch cards are widely used to promote the interests of charities and commercial concerns. They provide a useful mechanism for introducing many key concepts typically met by students in a first or second level under-graduate course involving probability modelling. The work described here stems from a real marketing problem. Simple card layouts lead quickly to consideration of combinatorial counting techniques, the probability of a player winning, and the expected value of a win. From a company viewpoint, assessing the risk of exceeding its prize money budget requires modelling of the distribution of total payout. The Binomial and Normal models are relevant here, while establishing expected payout and variation in payout highlight properties of expectation and variance. Simulation may also be used to support theoretical results.