Question

Condition of public school facilities. The National Center for Education Statistics (NCES) conducted a survey on the condition of America’s public school facilities. The survey revealed the following information. The probability that a public school building has inadequate plumbing is .25. Of the buildings with inadequate plumbing, the probability that the school has plans for repairing the building is .38. Find the probability that a public school building has inadequate plumbing and will be repaired.

Short answer

The probability is 0.095.

Step-by-step solution

Important formula

The formula is $\mathbf{P}\mathbf{(}\mathbf{A}\mathbf{\cap }\mathbf{B}\mathbf{)}\mathbf{=}\mathbf{P}\mathbf{(}\mathbf{A}\mathbf{)}\mathbf{.}\mathbf{P}\mathbf{\left(}\mathbf{B}\mathbf{\right|}\mathbf{A}\mathbf{)}$.

The probability that a public school building has inadequate plumbing and will be repaired.

Here, $\mathrm{P}\left(\mathrm{G}\right)=0.25=$chances of having inadequate plumbing.

$\mathrm{P}\left(\mathrm{F}|\mathrm{G}\right)=0.38=$ The school has plans to repair it.

$\begin{array}{c}\mathrm{P}(\mathrm{G}\cap \mathrm{F})=\mathrm{P}\left(\mathrm{G}\right)\times \mathrm{P}\left(\mathrm{F}\right|\mathrm{G})\\ =\left(0.38\right)\left(0.25\right)\\ =0.095\end{array}$

Therefore the probability is 0.095.