Occurrences of windstorms in an area are modeled as random phenomena. For simpli

Question

Occurrences of windstorms in an area are modeled as random phenomena. For simplicity, assume that any potential storm in a given time period in the area can be either strong (event Es), moderate (event EM), or weak (event Ew). These are the only three possibilities (mutually exclusive, collectively exhaustive) in our sample space. From past records, data suggested that PCEs) 0.01, P(EM) = 0.20, and P(EW) 0.79. A billboard is located in the area. If a strong storm occurs, the probability of failure of the billboard is 0.995. However, if the storm is moderate or weak, the failure probabilities are 0.056 and 0.001, respectively. Use F to denote the event of a billboard failure. If the billboard fails in a recent storm, what is the probability that a moderate storm has occurred? b.

Explanation / Answer

a) Probability of failure = P(F/ES)*P(ES)+ P(F/EW)*P(EW)+ P(F/EM)*P(EM) = 0.01*0.995+0.20*0.056+0.79*0.001=0.02194

b) P(M/F) = 0.20*0.056/0.02194=0.5104

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