Chapter 13.6, Problem 24HP

To determine

The probability of the household which has both high speed internet and cable television.

Answer to Problem 24HP

The probability of having both in the households is $\frac{19}{48}$ or $\mathrm{0.3958.}$

Explanation of Solution

In the given sample,

The probability of household having high speed internet, $P\left(\text{Internet}\right)=\frac{95}{150}$

The probability of household having cable television, $P\left(\text{Cable}\right)=\frac{125}{200}$

So, the probability of household that has both high speed internet as well as cable television $P\left(\text{Both}\right)$ is given as,

  $P\left(\text{Both}\right)=P\left(\text{Internet}\right)\times P\left(\text{Cable}\right)$

So,

  $\begin{array}{l}P\left(\text{Both}\right)=\frac{{95}^{19}}{{150}_6}\times \frac{{125}^3}{{300}_{{40}_8}}\\ P\left(\text{Both}\right)=\frac{19}{6\times 8}\text{or}\frac{19}{48}\\ P\left(\text{Both}\right)=0.3958\end{array}$

Conclusion:

Hence, the probability of having both in the households is $\frac{19}{48}$ or $\mathrm{0.3958.}$