(i) The greatest number of books that could be read is 12. The probability that a member reads this number of books is given by \(P(12) = (0.7)^{12}\).

Calculating this gives \(P(12) = 0.0138\).

(ii) To find the probability that a member reads fewer than 10 books, we calculate \(1 - P(10, 11, 12)\).

Using the binomial probability formula, we have:

\(P(10) = \binom{12}{10} (0.7)^{10} (0.3)^2\)

\(P(11) = \binom{12}{11} (0.7)^{11} (0.3)^1\)

\(P(12) = (0.7)^{12}\)

Thus, \(P(10, 11, 12) = \binom{12}{10} (0.7)^{10} (0.3)^2 + \binom{12}{11} (0.7)^{11} (0.3) + (0.7)^{12}\).

Calculating these probabilities gives \(P(10, 11, 12) = 0.2528\).

Therefore, the probability that a member reads fewer than 10 books is \(1 - 0.2528 = 0.747\).