Let the random variable \(X\) represent the number of adults who travel to work by car in a sample of 12. \(X\) follows a binomial distribution with parameters \(n = 12\) and \(p = 0.6\).

We need to find \(P(X < 10)\), which is equivalent to \(1 - P(X \geq 10)\).

Calculate \(P(X \geq 10) = P(X = 10) + P(X = 11) + P(X = 12)\).

Using the binomial probability formula:

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

\(P(X = 10) = \binom{12}{10} (0.6)^{10} (0.4)^2 = 0.063852\)

\(P(X = 11) = \binom{12}{11} (0.6)^{11} (0.4)^1 = 0.017414\)

\(P(X = 12) = \binom{12}{12} (0.6)^{12} (0.4)^0 = 0.0021768\)

Thus, \(P(X \geq 10) = 0.063852 + 0.017414 + 0.0021768 = 0.083443\).

Therefore, \(P(X < 10) = 1 - 0.083443 = 0.917\).