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A bridge can be damaged either due to failure in its foundation (event F) or superstructure (event S). The probabilities of these failures for the

A bridge can be damaged either due to failure in its foundation (event F) or superstructure (event S). The probabilities of these failures for the bridge are P(F)=0.008 and P(S)=0.005. It is also found that if there is failure in the foundation, the probability of failure in the superstructure is 0.50. (a) What is the probability of damage of the bridge? (b) What is the probability of damage of the bridge if F and S are statistically independent?

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