A computer system uses passwords that are exactly seven characters and each character is one of the 26 letters (a-z) or 10 integers (0-9). You maintain a password for this computer system. Let A denote the subset of passwords that begin with a vowel (either a, e, i, o, or u) and let B denote the subset of passwords that end with an even number (either 0, 2, 4, 6, or 8).

a) Suppose a hacker selects a password at random. What is the probability that your password is selected?

(b) Suppose a hacker knows your password is in event A and selects a password at random from this subset. What is the probability that your password is selected?

(c) Suppose a hacker knows your password is in A and B and selects a password at random from this subset. What is the probability that your password is selected?

### Solution

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