Chapter 17, Problem 13E

To determine

To find: the number of calls would be appropriate for the researchers, until selecting a first cardholder to take the double miles incentive.

Answer to Problem 13E

20

Explanation of Solution

Given:

  $\begin{array}{c}P\left(C\right)=0.10\\ P\left(D/C\right)=0.50\end{array}$

Formula used:

  $P\left(C\cap D\right)=P\left(D/C\right)\times P\left(C\right)$

  $E\left(X\right)=\frac{1}{p}$

Calculation:

  $\begin{array}{c}P\left(C\cap D\right)=P\left(D/C\right)\times P\left(C\right)\\ =\left(0.10\right)\left(0.50\right)\\ =0.05\end{array}$

Suppose X = The number of the owner of the card who will not take the first.

Therefore, X is a geom. (0.05)

Before the first card holder is identified to take double miles of promotion, researcher will have to make the planned amount of calls,

  $\begin{array}{c}E\left(X\right)=\frac{1}{p}\\ =\frac{1}{0.05}\\ =20\end{array}$