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