(a) To find \(P(X = 4)\), we need the probability that the first 3 spins do not result in a 2, and the 4th spin does. The probability of not getting a 2 on a single spin is \(\frac{4}{5}\), and the probability of getting a 2 is \(\frac{1}{5}\). Therefore,

\(P(X = 4) = \left( \frac{4}{5} \right)^3 \left( \frac{1}{5} \right) = (0.8)^3 (0.2) = 0.1024 = \frac{64}{625}.\)

(b) To find \(P(X < 6)\), we calculate the probability of getting a 2 within the first 5 spins. This is the complement of not getting a 2 in the first 5 spins:

\(P(X < 6) = 1 - (0.8)^5.\)

Calculating this gives:

\(P(X < 6) = 1 - 0.8^5 = 1 - 0.32768 = 0.67232.\)