Chapter 8.5, Problem 79E

Probability In Exercises 77-80, consider $n$ independent trials of an experiment in which each trial has two possible outcomes: “success” or “failure.” The probability of a success on each trial is $p$, and the probability of a failure is $q=1-p$. In this context, the term $C{}_k{p}^k{q}^{n-k}$ in the expansion of ${\left(p+q\right)}^n$ gives the probability of $k$ successes in the $n$ trials of the experiment.

The probability of a sales representative making a sale with any one customer is $\frac{1}{3}$. The sales representative makes eight contacts a day. To find the probability of making four sales, evaluate the term $C{}_4{\left(\frac{1}{3}\right)}^4{\left(\frac{2}{3}\right)}^4$ in the expansion of ${\left(\frac{1}{3}+\frac{2}{3}\right)}^8.$