Suppose that there is a chance for a newly constructed building to...

Let $\mathrm{E}_1=$ design is faulty $\mathrm{E}_2=$ design is not faulty $\mathrm{A}^2=$ building is collapses Since, $P\left(E_1\right)=10 \%=\frac{1}{10}$$\begin{aligned} & \mathrm{P}\left(\mathrm{E}_2\right)=90 \%=\frac{9}{10} \\ & \mathrm{P}\left(\mathrm{ A} / \mathrm{E}_1\right)=95 \%=\frac{19}{20} \\ & \mathrm{P}\left(\mathrm{ A} / \mathrm{E}_2\right)=45 \%=\frac{9}{20} \end{aligned}$$$Now$P\left(\frac{E}{A}\right)=\frac{P\left(E_1\right) P\left(A / E_1\right)}{P\left(E_1\right) \cdot P\left(A / E_1\right)+P\left(E_2\right) P\left(A / E_2\right)}=\frac{\frac{1}{10} \times \frac{19}{20}}{\frac{1}{10} \times \frac{19}{20}+\frac{9}{10} \times \frac{9}{20}}=\frac{19}{100}=0.19$