(a) The probability that it does not rain on Sunday is \(0.6\). If it does not rain on any day, the probability for each subsequent day is \(0.8\). Therefore, the probability that it does not rain on any of the 4 days is:

\(P(\text{no rain}) = 0.6 \times 0.8^3 = \frac{192}{625}\)

(b) The probability that it does not rain on Sunday is \(0.6\). The probability that it rains on Tuesday, given it did not rain on Monday, is \(0.2\). Therefore, the probability that the first day it rains is Tuesday is:

\(0.6 \times 0.8 \times 0.2 = \frac{12}{125}\)

(c) The probability that it rains on exactly one of the 4 days can be calculated by considering the scenarios where it rains on one specific day and not on the others. The scenarios are:

• Rains on Sunday: \(0.4 \times 0.3 \times 0.8 \times 0.8 = \frac{48}{625}\)
• Rains on Monday: \(0.6 \times 0.2 \times 0.3 \times 0.8 = \frac{18}{625}\)
• Rains on Tuesday: \(0.6 \times 0.8 \times 0.2 \times 0.3 = \frac{18}{625}\)
• Rains on Wednesday: \(0.6 \times 0.8 \times 0.8 \times 0.2 = \frac{48}{625}\)

Adding these probabilities gives:

\(\frac{48}{625} + \frac{18}{625} + \frac{18}{625} + \frac{48}{625} = \frac{132}{625}\)