Let the random variable \(X\) represent the number of children who own a bicycle. \(X\) follows a binomial distribution with parameters \(n = 15\) and \(p = 0.65\).

We need to find \(P(X > 12) = P(X = 13) + P(X = 14) + P(X = 15)\).

Using the binomial probability formula:

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

Calculate each probability:

\(P(X = 13) = \binom{15}{13} (0.65)^{13} (0.35)^2\)

\(P(X = 14) = \binom{15}{14} (0.65)^{14} (0.35)^1\)

\(P(X = 15) = \binom{15}{15} (0.65)^{15} (0.35)^0\)

Summing these probabilities gives:

\(P(X > 12) = 0.0617\)