(a) The probability of not getting a 3 on a single spin is \(\frac{4}{5}\). The probability of getting a 3 on the 8th spin for the first time is \(\left( \frac{4}{5} \right)^7 \times \frac{1}{5}\). This evaluates to \(\frac{16384}{390625}\) or approximately 0.0419.

(b) The probability of getting a 3 for the first time in fewer than 6 spins is the complement of not getting a 3 in the first 5 spins. This is calculated as:

\(1 - \left( \frac{4}{5} \right)^5\)

Alternatively, it can be calculated using the sum of probabilities for getting a 3 on each of the first 5 spins:

\(\frac{1}{5} + \frac{4}{5} \times \frac{1}{5} + \left( \frac{4}{5} \right)^2 \times \frac{1}{5} + \left( \frac{4}{5} \right)^3 \times \frac{1}{5} + \left( \frac{4}{5} \right)^4 \times \frac{1}{5}\)

This evaluates to \(\frac{2101}{3125}\) or approximately 0.672.