(a) Let the random variable X be the number of days with more than 10 cm of rain in a 7-day period. X follows a binomial distribution with parameters n = 7 and p = 0.18. We need to find P(X > 2).

\(P(X > 2) = 1 - P(X \leq 2) = 1 - (P(X = 0) + P(X = 1) + P(X = 2)).\)

Using the binomial probability formula, we calculate:

\(P(X = 0) = \binom{7}{0} (0.18)^0 (0.82)^7 = 0.249285,\)

\(P(X = 1) = \binom{7}{1} (0.18)^1 (0.82)^6 = 0.383048,\)

\(P(X = 2) = \binom{7}{2} (0.18)^2 (0.82)^5 = 0.252251.\)

\(Thus, P(X \leq 2) = 0.249285 + 0.383048 + 0.252251 = 0.884584.\)

\(Therefore, P(X > 2) = 1 - 0.884584 = 0.115.\)

(b) Let Y be the number of 7-day periods with at least one day of more than 10 cm of rain. The probability of at least one day of rain in a 7-day period is 1 - P(X = 0) = 1 - 0.82^7 = 0.7507.

\(Y follows a binomial distribution with parameters n = 3 and p = 0.7507. We need to find P(Y = 2).\)

\(P(Y = 2) = \binom{3}{2} (0.7507)^2 (1 - 0.7507)^1 = 3 \times 0.7507^2 \times 0.2493 = 0.421.\)