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HW3 SolutionProblem 1From lecture, you can assess these subjective probabilities via the indirect method whereyou vary the probability of one of the lotteries until the individual is indifferent betweenboth lotteries.This is the table that is given to you.In one of the lotteries the assesseewins if the wind speedexceedsa thresholdq.When the assessee is indifferent, we getP(Wind> q) =p. Therefore, we have the following:1.q= 10→p= 0.95⇒P(Wind≤q) = 0.052.q= 20→p= 0.65⇒P(Wind≤q) = 0.353.q= 25→p= 0.55⇒P(Wind≤q) = 0.454.q= 35→p= 0.45⇒P(Wind≤q) = 0.55Below is the graph:1
Problem 2You are given the following probabilities:1. If we have no ROS, we get flooding if•Levees fail, call it event L: D or C or (A and B)⇔D or C or (A|B and B) or•Pumps fail, call it event P: F or (G and H)P(Flood|wind >30,¬ROS) =P(L∪P|wind >30,¬ROS)P(L) =P(D∪C∪(A∩B))=P(D) +P(C) +P(A∩B)-P(D)P(C)-P(D)P(A∩B)-P(C)P(A∩B)=.01 +.1 +.24-.01(.1)-.01(.24)-.1(.24) +.01(.1)(.24)= 0.32284P(P) =P(F∪(G∩H))=P(F) +P(G∩H)-P(F∩G∩H)=P(F) +P(G)P(H)-P(F)P(G)P(H)=.8 +.7(.1)-.7(.1)(.8)= 0.814Therefore,P(L∪P