Maths Extension 1

So far we have worked from first principles. In many cases we can describe the pattern of outcomes from a series of random experiments with a mathematical model (ie. with an equation) and exploit the model to calculate probabilities more easily than with recourse to the first principles. The binomial distribution is a case in point as it allows a ready formula to calculate probabilities of the number of successes from $n$ trials. Once again, it is important to establish notation carefully so the formula can be used correctly.

$$P(X=r) = {{n} \choose r}p^r (1-p)^{n-r}$$