Problem 5 (10 points):
A computer system uses passwords that are six characters, and each character is one of the 26 letters (a-z) or 10 integers (0-9). Uppercase letters are not used. Let A denote the event that a password begins with a vowel (either a, e, i, o, or u), and let B denote the event that a password ends with an even number (either 0, 2, 4, 6, or 8). Suppose a hacker selects a password at random. Determine the following probabilities:
(a) P(A)
(b) P(B)
(c) P(A $\cap$ B)
(d) P(A $\cup$ B)