Graduate Problem 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) Therefore, P(exactly one integer or exactly two integers)=0.377 +0.254 - 0.630 2.5.8.​