Question

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.

Disaster Magnitude	Light Debris	Moderate Debris	Heavy Debris	Total
Low	80	15	5	100
Moderate	50	40	10	100
High	30	50	20	100
Total	160	105	35	300

(a) What is the probability that a randomly selected road is under moderate debris after an earthquake?

Round your answer to two decimal places (e.g. 98.76).

(b) What is the probability that a randomly selected road is under moderate or heavy debris after an earthquake?
Round your answer to two decimal places (e.g. 98.76).

Answer 1

(a) Probability that a randomly selected road is under moderate debris after an earthquake = Number of roads being under moderate debris after an earthquake / Total number of roads under debris

Disaster Magnitude	Light Debris	Moderate Debris	Heavy Debris	Total
Low	80	15	5	100
Moderate	50	40	10	100
High	30	50	20	100
Total	160	105	35	300

From the above table:

Number of roads being under moderate debris after an earthquake = 105

Total number of roads under debris = 300

Probability that a randomly selected road is under moderate debris after an earthquake = Number of roads being under moderate debris after an earthquake / Total number of roads under debris = 105/300 = 0.35

Probability that a randomly selected road is under moderate debris after an earthquake = 0.35

(b)

Probability that a randomly selected road is under moderate or heavy debris after an earthquake = Probability that a randomly selected road is under moderate debris after an earthquake + Probability that a randomly selected road is under heavy after an earthquake

From (a)

Probability that a randomly selected road is under moderate debris after an earthquake = 105/300 = 0.35

Probability that a randomly selected road is under heavy debris after an earthquake = Number of roads being under heavy debris after an earthquake / Total number of roads under debris

Disaster Magnitude	Light Debris	Moderate Debris	Heavy Debris	Total
Low	80	15	5	100
Moderate	50	40	10	100
High	30	50	20	100
Total	160	105	35	300

From the above table,

Number of roads being under heavy debris after an earthquake = 35

Total number of roads under debris = 300

Probability that a randomly selected road is under heavy debris after an earthquake = Number of roads being under heavy debris after an earthquake / Total number of roads under debris = 35/300 =0.12

Probability that a randomly selected road is under moderate or heavy debris after an earthquake

= Probability that a randomly selected road is under moderate debris after an earthquake + Probability that a randomly selected road is under heavy after an earthquake

= 0.35+0.12 = 0.47

Probability that a randomly selected road is under moderate or heavy debris after an earthquake = 0.47