(a) To find the probability that exactly one marble is yellow, consider the arrangements: YGG, GYG, GGY. The probability for each arrangement is:

\(\frac{5}{9} \times \frac{4}{8} \times \frac{3}{7}\)

Multiply by 3 for the three arrangements:

\(3 \times \frac{5}{9} \times \frac{4}{8} \times \frac{3}{7} = \frac{180}{504} = \frac{5}{14}\)

(b) The probability distribution table for \(X\) is:

(c) The expected value \(E(X)\) is calculated as:

\(E(X) = 0 \times \frac{1}{21} + 1 \times \frac{5}{14} + 2 \times \frac{10}{21} + 3 \times \frac{5}{42} = 1.67\)