(a) To find the probability that Georgie wears a hat, we calculate the total probability of wearing a hat with each scarf:

\(P(H) = 0.2 \times 1 + 0.45 \times 0.4 + 0.35 \times 0.3\)

\(= 0.2 + 0.18 + 0.105\)

\(= 0.485\)

Thus, the probability that Georgie wears a hat is \(\frac{97}{200}\) or 0.485.

(b) To find the probability that Georgie wears a yellow scarf given that she does not wear a hat, we use conditional probability:

\(P(Y | \overline{H}) = \frac{P(Y \cap \overline{H})}{P(\overline{H})}\)

\(P(Y \cap \overline{H}) = 0.35 \times 0.7 = 0.245\)

\(P(\overline{H}) = 1 - P(H) = 1 - 0.485 = 0.515\)

\(P(Y | \overline{H}) = \frac{0.245}{0.515} \approx 0.476\)

Thus, the probability that Georgie wears a yellow scarf given that she does not wear a hat is \(\frac{49}{103}\) or 0.476.