Answer:
a. Binomial random variable (n=4, p=0.25)
b. Attached.
c. X=1
Explanation:
This can be modeled as a binomial random variable, with parameters n=4 (size of the sample) and p=0.25 (proportion of homeowners that are insured against earthquake damage).
a. The probability that X=k homeowners, from the sample of 4, have eartquake insurance is:

The sample space for X is {0,1,2,3,4}
The associated probabilties are:

b. The histogram is attached.
c. The most likely value for X is the expected value for X (E(X)).
Is calculated as:
