Chapter 12.5, Problem 35HP

To determine

To find the number of bulbs that can be strung together with at least $90\%$ chance that the whole string will light.

Answer to Problem 35HP

The number of bulbs required is $21$ .

Explanation of Solution

Given information:

The given statement is:

“In some cases, if one bulb in a string of holiday lights fails to work, the whole string will not light. If each bulb in a set has a $99.5\%$ chance of working, what is the maximum number of lights that can be strung together with at least a $90\%$ chance that the whole string will light?”

Calculation :

Let the number of bulbs required be $\text{n}$ .

Multiply the probability of each bulb with the number of bulbs, and equate it with the probability of the string working.

  $\begin{array}{l}{\left(\frac{99.5}{100}\right)}^{\text{n}}=\frac{90}{100}\\ {0.995}^{\text{n}}=0.90\\ \text{n}=21\end{array}$

Hence, the number of bulbs required is $21$ .