Question

do in paper

8. An article in the Transportation Research Part E Journal ["Arc Routing Problems to Restore Connectivity of a Road Network" (2016)] considered ways of re-establishing the connectivity of road networks after a natural disaster- earthquake. Estimates of the probabilities of a randomly chosen road being under light debris, moderate debris, and heavy debris conditions after different disaster magnitudes are shown in the following table. Disaster magnitude is equally likely to be low, moderate or high. Total IS 5 100 Disaster Light Moderate Heavy Magnitude Debris Debris Debris Low Moderate 50 40 10 High 30 50 120 Total 160 105 35 100 100 300 Given that a road had heavy debris after an earthquake, what is the conditional probability that the disaster magnitude was high?

Answer 1

Prob.(disaster management was high | a road had heavy debris after an earthquake)
= Prob.(disaster management was high and the road had heavy debris)/Prob.(road had heavy debris)
= (20/300)/(35/200) = 20/35 = 4/7 = 0.5714.