Let the random variable \(X\) represent the number of wet days in a 10-day period. \(X\) follows a binomial distribution with parameters \(n = 10\) and \(p = 0.16\).

We need to find \(P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)\).

Using the binomial probability formula:

\(P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}\)

Calculate each probability:

\(P(X = 0) = \binom{10}{0} (0.16)^0 (0.84)^{10} = 0.17490\)

\(P(X = 1) = \binom{10}{1} (0.16)^1 (0.84)^9 = 0.333145\)

\(P(X = 2) = \binom{10}{2} (0.16)^2 (0.84)^8 = 0.28555\)

Summing these probabilities gives:

\(P(X < 3) = 0.17490 + 0.333145 + 0.28555 = 0.794\)