14. Independent trials that result in a success with probability p are successively performed until a total of r successes is obtained. Show that the probability that exactly n trials are required is

$$

\binom{n-1}{r-1} p^r (1-p)^{n-r}

$$

Use this result to solve the problem of the points (Example 4i).

HINT: In order for it to take n trials to obtain r successes, how many successes must occur in the first n – 1 trials?