Three areas of southern California are prime candidates for forest fires each dry season. You believe (based on historical evidence) that each of these areas, independently of the others, has a 30% chance of having a major forest fire in the next dry season.
a. Find the probability distribution of X, the number of the three regions that have major forest fires in the next dry season.
b. What is the probability that none of the areas will have a major forest fire?
c. What is the probability that all of them will have a major forest fire?
d. What is expected number of regions with major forest fires?