(Solved): The truss bridge shown in the figure below is subjected to gravity and live loads which are uncerta ...

The truss bridge shown in the figure below is subjected to gravity and live loads which are uncertain/random and the tensile strengths of the truss members are also uncertain/random. Assuming that: (1) the bridge supports cannot fail, (2) the probability of failure of each truss member is 0.5 percent, and (3) the failures of individual members are mutually statistically independent random events, compute the probability of bridge failure in two different ways and comment on your results. Hint: You may find useful the following formula from combinatorics: $\left(\begin{array}{l}\mathrm{N}\\ \mathrm{k}\end{array}\right)=\frac{\mathrm{N}(\mathrm{N}-1)\dots (\mathrm{N}-\mathrm{k}+1)}{\mathrm{k}!}=\frac{\mathrm{N}!}{\mathrm{k}!(\mathrm{N}-\mathrm{k})!}$ where $\left(\begin{array}{l}N\\ k\end{array}\right)$ is referred to as the binomial coefficient which can be defined as the number of possible subsets of $k$ different elements (regardless of their order) drawn from a set of $\mathrm{N}$ distinguishable elements.