Question 5 (18 points) A provincial transportation agency is considering whether to repair an old bridge or not. The engineering assessment showed that the probability that the bridge collapses in the next 50 years is 20%. However, if one earthquake happens during this period, the likelihood of the bridge collapsing will increase to 55%. If the area experiences two or more earthquakes in the analysis Page 3 of 4 period (50 years), the likelihood of the bridge collapsing will increase to 80%. The total cost associated with the bridge collapse was estimated to be $ 80 million. The transportation agency can repair the bridge which will reduce the probability of collapse to 2% if no earthquake occurs in the upcoming 50 years. The probability of the bridge collapsing after repair increases to 9% if one earthquake occurs and 18% if two or more earthquakes occur during the analysis period (50 years). The Geological studies indicated that earthquake occurrence in this region follows the Poisson distribution (P(x)= with a rate of an earthquake every 200 years. Based on this information, what is the maximum cost that the transportation agency should pay to repair the bridge? emm x X