The probability of rolling a 1 or 2 is \(\frac{2}{6}\), and the probability of rolling a 3, 4, 5, or 6 is \(\frac{4}{6}\).

For bag A, the probability of picking two white marbles is:

\(\frac{8}{15} \times \frac{7}{14}\)

For bag B, the probability of picking two white marbles is:

\(\frac{6}{15} \times \frac{5}{14}\)

The total probability that both marbles are white is:

\(\frac{2}{6} \times \frac{8}{15} \times \frac{7}{14} + \frac{4}{6} \times \frac{6}{15} \times \frac{5}{14}\)

Calculating each part:

\(\frac{2}{6} \times \frac{8}{15} \times \frac{7}{14} = \frac{56}{630}\)

\(\frac{4}{6} \times \frac{6}{15} \times \frac{5}{14} = \frac{60}{630}\)

Adding these probabilities gives:

\(\frac{56}{630} + \frac{60}{630} = \frac{116}{630} = \frac{58}{315}\)

Thus, the probability that both marbles are white is \(\frac{58}{315}\) or 0.184.