Let the probability that an adult does not wear a watch be 0.09. We are dealing with a binomial distribution where the number of trials is 14 and the probability of success (an adult not wearing a watch) is 0.09.

We need to find the probability that more than 2 adults do not wear a watch, which is equivalent to finding:

\(P(X > 2) = 1 - P(X \leq 2)\)

Calculate \(P(X \leq 2)\) as follows:

\(P(X = 0) = (0.91)^{14}\)

\(P(X = 1) = \binom{14}{1} (0.09)^1 (0.91)^{13}\)

\(P(X = 2) = \binom{14}{2} (0.09)^2 (0.91)^{12}\)

Thus,

\(P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)\)

Substitute the values:

\(P(X = 0) = 0.2670\)

\(P(X = 1) = 0.3698\)

\(P(X = 2) = 0.2377\)

Therefore,

\(P(X \leq 2) = 0.2670 + 0.3698 + 0.2377 = 0.8745\)

Finally,

\(P(X > 2) = 1 - 0.8745 = 0.1255\)

Rounding to three decimal places, the probability is 0.126.