The probability of event A, where the white marble is in either box L or M, is given by:

\(P(A) = \frac{1}{2}\)

The probability of event B, where the red marble is to the left of both the green marble and the yellow marble, is given by:

\(P(B) = \frac{8}{24} = \frac{1}{3}\)

The probability of both events A and B occurring together is:

\(P(A \cap B) = \frac{1}{6}\)

To check for independence, we verify if:

\(P(A) \times P(B) = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}\)

Since \(P(A \cap B) = P(A) \times P(B)\), events A and B are independent.