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). Let Ω denote the set of all possible password, and let A and B denote the events that consist of passwords with only letters or only integers, respectively. Suppose that all passwords in Ω are equally likely. Determine the following probabilities:

(a) P(A|B′)

(b) P(A' ∩ B)

(c) P (password contains exactly 2 integers given that it contains at least 1 integer)