A cable is employed as a tension member in infrastructure system. There are three kinds of cables which could be employed as the tension member: one that has 70 kN resistance, one with 80 kN resistance, and one with 90 kN resistance. The cable kinds are equally likely to be chosen as tension member. A load will be applied to infrastructure system, and there are three equal possibilities for this load: 65 kN, 76 kN, or 85 kN. (adapted from [Khisty et al. 2012])
a. Determine the probability that the resistance of such a cable chosen at random will be at least equal to 80 kN?
b. Determine the probability that the load will be at most equal to 75 kN?
c. Determine the probability of failure of randomly chosen cable (where failure is defined as the applied load outweighing the cable resistance)?