## Related questions with answers

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 $_{n} C_{k} p^{k} q^{n-k}$ in the expansion of $(p + q)^n$ gives the probability of k successes in the n trials of the experiment. The probability of a sales representative making a sale to 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 $_{8} C_{4}\left(\frac{1}{3}\right)^{4}\left(\frac{2}{3}\right)^{4}$ in the expansion of $\left(\frac{1}{3}+\frac{2}{3}\right)^{8}$

Solution

VerifiedIn this task we have to calculate the probability of making four sales where the sales representative makes eight contacts a day.

We can find that probability by evaluating the term

$_{8}C_{4}\left(\frac{1}{3}\right)^{4}\left(\frac{2}{3}\right)^{4}$

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