Question

4. The National fire incident reporting service reports that, among residential fires, approximately 73% are in family homes, 20% are in apartments, and the other 7% are in other types of dwellings. If four fires are independably reported in one day, Find the probability that two are in family homes, one is in an apartment, and one is in another type of dwelling. The typical cost of damage for a fire in a family home is $20,000, the typical cost for an apartment fire is $10,000, and the typical cost for a fire in other dwellings is only $2,000, find the expected total damage cost for four independently reported fires. a. b.

Answer 1

a) Probability = 4C2 * 0.73² * 2C1 * 0.2 * 0.07 = 0.0895

b) Expected value = 4 * (20000 * 0.73 + 10000 * 0.2 + 2000 * 0.07) = $66960