# Re-establishing Road Network Connectivity After a Natural Disaster: A Probabilistic Approach

Given that a road had light debris after an earthquake, what is the conditional probability that the disaster magnitude was low?

The conditional probability that the disaster **magnitude** was low, given that a road had light debris after an **earthquake**, is approximately 0.33.

An article in the Transportation Research Part E Journal considered ways to re-establish the connectivity of road networks after a natural disaster, specifically an earthquake. The study focused on estimating probabilities of roads being under different debris conditions after varying disaster magnitudes.

To determine the conditional probability of the disaster magnitude being low given light debris on a road after an earthquake, Bayes' theorem was applied. Let P(A) represent the probability of the disaster magnitude being low and P(B) denote the probability of a road having light debris.

Given that the disaster magnitude is equally likely to be low, moderate, or high (each with a probability of 1/3), P(A) = 1/3. The probability of a road having light debris (P(B)) was provided in the table as 0.2.

The calculation of the conditional probability P(A|B) involves the probability of light debris given a low disaster magnitude (0.2), multiplied by the probability of a low disaster magnitude, and divided by the probability of light debris. Substituting the values, the resulting conditional probability is approximately 0.33.

Understanding and correctly applying Bayes' theorem is essential in solving such probability problems, as demonstrated in this solution. It showcases the importance of interpreting data and utilizing mathematical principles to make informed decisions in post-disaster scenarios.