A computer system uses passwords that contain exactly eight characters, and each character is one of the 26 lowercase letters (a–z) or 26 uppercase letters (A–Z) or 10 integers (0–9). Assume all passwords are equally likely. Let A and B denote the events that consist of passwords with only letters or only integers, respectively. Determine the following probabilities:

(a) P(AUB)

(b) P(A'UB)

(c) P (Password contains exactly 1 or 2 integers)