Suppose that in a certain metropolitan area, 90% of all households have cable TV. Let x denote the number among four randomly selected households that have cable TV. Then x is a binomial random variable with n = 4 and p = 0.9. (Round your answers to four decimal places.)

a. Calculate p(2) = P(x = 2).

b. Interpret this probability.

i. This is the probability that at least 2 out of 4 selected households have cable TV.

ii. This is the probability that exactly 2 out of 10 selected households have cable TV.

iii. This is the probability that exactly 2 out of 4 selected households have cable TV.

iv. This is the probability that at least 2 out of 10 selected households have cable TV.

c. Calculate p(4), the probability that all four selected households have cable TV.

d. Determine P(x ≤ 3).