The element of chance enters into many of our attempts to understand the world we live in. A mathematical *theory of probability* allows us to calculate the likelihood of complex events if we assume that the events are governed by appropriate axioms. This theory has significant applications in all branches of science, and it has strong connections with the techniques we have studied in previous chapters.

Probabilities are called “discrete” if we can compute the probabilities of all events by summation instead of by integration. We are getting pretty good at sums, so it should come as no great surprise that we are ready to apply our knowledge to some interesting calculations of probabilities and averages.

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