Monitoring quality of power equipment. Mechanical Engineering (February 2005) reported on the need for wireless networks to monitor the quality of industrial equipment. For example, consider Eaton Corp., a company that develops distribution products. Eaton estimates that 90% of the electrical switching devices it sells can monitor the quality of the power running through the device. Eaton further estimates that of the buyers of electrical switching devices capable of monitoring quality, 90% do not wire the equipment up for that purpose. Use this information to estimate the probability that an Eaton electrical switching device is capable of monitoring power quality and is wired up for that purpose.

Step by step solution

01

Important formula

The formula for probability is$\mathbf{P}\mathbf{(}{\mathbf{A}}^c\mathbf{)}\mathbf{=}\mathbf{1}\mathbf{-}\mathbf{P}\mathbf{(}\mathbf{A}\mathbf{)}$.

02

The probability that an Eaton electrical switching device is capable of monitoring power quality and is wiredup for that purpose.

Here,$\mathrm{P}\left(\mathrm{A}\right)=90\mathrm{\%}=0.9$

$\mathrm{P}\left(\mathrm{B}|\mathrm{A}\right)=90\mathrm{\%}=0.9$

Now, find the result, then,

$\begin{array}{c}\mathrm{P}\left({\mathrm{B}}^{\mathrm{C}}\right|\mathrm{A})=1-\mathrm{P}({\mathrm{B}}^{\mathrm{C}}\left|\mathrm{A}\right)\\ =1-0.9\\ =0.1\\ \mathrm{P}(\mathrm{A}\cap {\mathrm{B}}^{\mathrm{C}})=\mathrm{P}\left({\mathrm{B}}^{\mathrm{C}}\right|\mathrm{A}\left)\mathrm{P}\right(\mathrm{A})\\ =(0.1)(0.9)\\ =0.09\end{array}$

Therefore, the probability is 0.09.

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