This question tests the fundamental concept of probability where P(E) = Number of favorable outcomes / Total number of possible outcomes. The total number of discs is 90 (numbered 1 to 90), which gives us the denominator for all three parts. For part (i), two-digit numbers range from 10 to 90, giving 81 numbers. For part (ii), perfect squares between 1 and 90 are 1, 4, 9, 16, 25, 36, 49, 64, 81 — totaling 9 numbers. For part (iii), numbers divisible by 5 form an arithmetic progression with 18 terms.