Chapter 17, Problem 12E

To determine

To find: The expected number of tests before a bad one is detected.

Answer to Problem 12E

50

Explanation of Solution

Given:

Geometric model.

Success = good chip, $p=0.98$ .

Failure = bad chip, $q=0.02$ .

Formula used:

  $E\left(X\right)=\frac{1}{p}$

Calculation:

Suppose X = Number of good chips until the first bad chip is being checked.

Therefore, X is geom. (0.02)

  $\begin{array}{c}E\left(X\right)=\frac{1}{p}\\ =\frac{1}{0.02}\\ =50\end{array}$

The number of chips checked before a bad one has been detected is estimated to be 50.