Consider the set S = \{0, 2, 6, 8, 9, d, n, s, x, z\}. An element of S is drawn at random. Expressing your answers exactly (use fractions rather than rounding), determine:
The probability that the element is a number =
The probability that the element is a letter =
The probability that the element is a number greater than 3 =
The probability that the element is a letter after k in the alphabet =
The probability that the element is a number greater than 3, given that the element is a number =
The probability that the element is a letter after k in the alphabet, given that the element is a letter =