One way to differentiate between probability and statistics posits that there is an inverse relationship between the problems considered by the two fields (the explanation is often attributed to mathematician Persi Diaconis). With probability, one studies an essential activity that includes some degree of randomness or uncertainty, and one uses probability to figure out what is likely to happen in certain circumstances. With statistics, something that has already happened is observed; the statistician hope to figure out the underlying process that provided the result. Thus probability deals with predicting the likelihood of future events, while statistics involves the analysis of past events.

Another way to understand this is to think of a jar filled with both black jelly beans and white jelly beans. The probabilist starts by knowing the proportion of black to white jelly beans in the jar and figures the probability of drawing, for example, two black jelly beans in a row. The statistician takes samples from the jar and infers the proportion of black to white jelly beans from the samples.

Demonstrate your understanding of this observation by inventing a business scenario that exemplifies the inverse relationship between probability and statistics. Enhance the explanation with quantitative information that supports your narrative. You will need to fabricate the information; just be sure it is realistic