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Unformatted text preview: P (S2)/ P (R)= 0.45 * 0.33/0.2485 = 0.5975 2/9 CEE 202 – Engineering Risk & Uncertainty Spring 2011 (Bond) Homework 3 Bayes’ Theorem and Probability Dist. 3) A small, old bridge is susceptible to damages from heavy trucks. Suppose the bridge can have room for at most two trucks, one in each lane. It can easily carry one truck, but it may be damaged when two trucks are present, and this depends on the extent of overloading. The damage probability is: 30% when both trucks are overloaded, 5% when one truck is overloaded, and 0.1% when neither truck is overloaded. The fraction of trucks entering the bridge that are overloaded is 10%. You can assume that the overloading of any two trucks has no relationship. Ans: This problem is easier if you think about two trucks separately. O = Overloaded N = Not overloaded OO = both trucks overloaded ON = truck 1 but not truck 2; NO truck 2 but not truck 1 NN = neither truck overloaded Given: P(O) = 0.1 for either truck ; trucks are statistically independent P(D  OO) = 0.3 P(D  NO) = P(D  ON) = 0.05 P(D  NN) = 0.001 a)
What is the probability of damage to the bridge while supporting two trucks? Total probability: P(D) = P(D  OO) * P(OO) + P(D  ON) * P(ON) + P (D  NO) * P(NO) + P(D  NN) * P(NN) = P(D  OO) * P(O) * P(O) + 2* P(D  ON) * P(O) * P(N) + P(D  NN) * P(N) * P(N) = 0.3 * 0.1 * 0.1 + 2 * 0.05 * 0.1 * 0.9 + 0.001 * 0.9 * 0.9 = 0.0128 (1.3 %) Answer: 0.013 b) If the bridge is damaged, what is the probability that it was c...
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 Spring '08
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