(a) The probability of obtaining a score of 17 or more in one throw is given by:

\(P(17 \text{ or } 18) = \frac{4}{216} = \frac{1}{54}\)

To find the probability that this score is first obtained on the 6th throw, we use the geometric distribution:

\(P(X = 6) = \left(\frac{53}{54}\right)^5 \times \frac{1}{54}\)

Calculating this gives:

\(P(X = 6) = 0.0169\)

(b) To find the probability that a score of 17 or more is obtained in fewer than 8 throws, we use the complement rule:

\(P(X < 8) = 1 - \left(\frac{53}{54}\right)^7\)

Calculating this gives:

\(P(X < 8) = 0.123\)

An alternative method involves summing probabilities for each throw from 1 to 7:

\(P(X < 8) = \left(\frac{1}{54}\right) + \left(\frac{53}{54}\right)\left(\frac{1}{54}\right) + \left(\frac{53}{54}\right)^2\left(\frac{1}{54}\right) + \ldots + \left(\frac{53}{54}\right)^6\left(\frac{1}{54}\right)\)

This also results in:

\(P(X < 8) = 0.123\)