To determine if events A and B are independent, we need to check if \(P(A \cap B) = P(A) \times P(B)\).

First, calculate \(P(A)\):

The possible outcomes for the sum of two dice being less than 6 are: (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (3,1), (3,2), (4,1). There are 10 outcomes.

Thus, \(P(A) = \frac{10}{36} = \frac{5}{18} \approx 0.278\).

Next, calculate \(P(B)\):

The possible outcomes for the difference between the numbers being at most 2 are: (1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (3,5), (4,2), (4,3), (4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), (6,4), (6,5), (6,6). There are 24 outcomes.

Thus, \(P(B) = \frac{24}{36} = \frac{2}{3} \approx 0.667\).

Now, calculate \(P(A \cap B)\):

The outcomes that satisfy both conditions are: (1,1), (1,2), (1,3), (2,1), (2,2), (3,1), (3,2), (4,1). There are 8 outcomes.

Thus, \(P(A \cap B) = \frac{8}{36} = \frac{2}{9} \approx 0.222\).

Check independence:

\(P(A) \times P(B) = \frac{5}{18} \times \frac{2}{3} = \frac{5}{27} \approx 0.185\).

Since \(P(A \cap B) \neq P(A) \times P(B)\), the events are not independent.