Question

An article in the Transportarion Research Part E Jounai 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. Disaster Light Moderate v Total Debris Debris Debris 00 5 5100 50 4010 100 30 50 20 100 60 105 300 Moderate Given that a road had light debris after an earthquake, what is the conditional probability that the disaster magnitude was high? Round your answer to two decimal places (e.a. 98.76)

Answer 1

We want to find the conditional probability that the disaster magnitude was high, given that a road had light debris after an earthquake.

P(High | Light debris)

= P(High And Light debris) / P(Light debris)

= (30/300) / (160/300)

= 30/160

= 0.1875

P(High | Light debris) = 0.1875

P(High | Light debris) = 0.19 ( rounded to two decimal places)