Chapter 11.9, Problem 14E

a.

To determine

To find the probability that both batteries in a pack are defective.

Answer to Problem 14E

The probability that both batteries in a pack are defective is $\frac{1}{39800}$

Explanation of Solution

Given information:

A company determined that $1\%$ of the batteries it sells are defective.

Calculation :

The probability of getting a defective battery is $\frac{1}{100}$ .

The probability of getting a defective battery from $200$ batteries is $\frac{1}{200}$ .

The probability of getting another defective battery from the remaining $199$ batteries is $\frac{1}{199}$

The probability of getting two effective batteries in a pack is $\frac{1}{200}\cdot \frac{1}{199}=\frac{1}{39800}$

Hence, the probability that both batteries in a pack are defective is $\frac{1}{39800}$

b.

To determine

To predict the number of packs in which both the batteries are defective.

Answer to Problem 14E

  $25$ packs can have both the batteries defective.

Explanation of Solution

Given information:

The company produces $1,000,000$ packs each year.

Calculation :

The number of packs in which both the batteries can turn out to be defective can be calculated by:

  $\begin{array}{l}\frac{1}{39,800}\times 1,000,000\\ 25.13\end{array}$

Hence, $25$ packs can have both the batteries defective