Let the random variable \(X\) represent the number of people who choose a mobile phone made by Company A. \(X\) follows a binomial distribution with parameters \(n = 13\) and \(p = 0.6\).

We need to find \(P(X < 11)\), which is equivalent to \(1 - P(X \geq 11)\).

Using the complement rule, \(P(X \geq 11) = P(X = 11) + P(X = 12) + P(X = 13)\).

Using the binomial probability formula:

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

Calculate each probability:

\(P(X = 11) = \binom{13}{11} (0.6)^{11} (0.4)^2\)

\(P(X = 12) = \binom{13}{12} (0.6)^{12} (0.4)^1\)

\(P(X = 13) = \binom{13}{13} (0.6)^{13} (0.4)^0\)

Thus, \(P(X \geq 11) = \binom{13}{11} (0.6)^{11} (0.4)^2 + \binom{13}{12} (0.6)^{12} (0.4)^1 + \binom{13}{13} (0.6)^{13}\).

Calculate \(P(X < 11) = 1 - P(X \geq 11)\).

\(P(X < 11) = 1 - (\binom{13}{11} (0.6)^{11} (0.4)^2 + \binom{13}{12} (0.6)^{12} (0.4)^1 + \binom{13}{13} (0.6)^{13})\)

\(P(X < 11) = 0.942\).