If the overnight letter arrived late, what is the probability that it was via A?

Question

If the overnight letter arrived late, what is the probability that it was via A? Via B? Via C? Delay (D) in a consideration project can be by material shortage (M) labor shortage (L), and bad weather (W); the probability are 40%, 40%, and 20%, respectively. Assume M, L, and W are mutually exclusive and collectively exhaustive, and the likelihood of their occurrence is 2:2:1, respectively. What is the probability of delay of the consideration? If the project was delayed, what is the probability that the delay was caused by bad weather? The safety of a dam depends on the load conditions produced by water levels upstream and downstream. These load conditions can be denoted as dewatering (D) overlapping (o), and flat-top pool condition (F). In a typical year consisting of 365 days, these load condition can occur on 3, 62, and 300 days, respectively. The probability of failure of the dam in each

Explanation / Answer

part a.) probability of delay in the construction = (M)*(~L)*(~W) + (~M)*(L)*(~W) + (~M)*(~L)*(W) {since mutually exclusive }

= 0.4*0.6*0.8 + 0.6*0.4*0.8 + 0.6*0.6*0.2 = 0.192 + 0.192 + 0.072 = 0.456

part b.) probability of bad weather = 1 / (2+2+1) = 1/5 = 0.2

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