Let the probability of a bag being underweight be \(p = 0.1\). The number of underweight bags follows a binomial distribution \(X \sim B(10, 0.1)\).

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:

\(P(X = 0) = \binom{10}{0} (0.1)^0 (0.9)^{10} = 0.348678\)

\(P(X = 1) = \binom{10}{1} (0.1)^1 (0.9)^9 = 0.38742\)

\(P(X = 2) = \binom{10}{2} (0.1)^2 (0.9)^8 = 0.19371\)

Sum these probabilities:

\(P(X < 3) = 0.348678 + 0.38742 + 0.19371 = 0.929808\)

Rounding to three decimal places, the probability is \(0.930\).