The article \"Expectation Analysis of the Probability of Failure for Water Supply Pipes\" (J. of Pipeline Systems Engr. and Practice, May 2012: 3646) proposed using the Poisson distribution to model the number of failures in pipelines of various types. Suppose that for cast-iron pipe of a particular length, the expected number of failures is 1 (very close to one of the cases considered in the article). Then X, the number of failures, has a Poisson distribution with ,u = 1. a. Obtain P(X S 5). L n-n.-__-.._- '1fo I")\\