A two-digit number is picked at random, every two-digit number being equally likely. What is the probability that it is divisible by 4 but NOT by 6?

The two-digit numbers run from 10 to 99, so there are 90 of them. Multiples of 4 among these run 12, 16, …, 96 — that is 22 numbers. Those divisible by both 4 and 6 are the multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96 — 8 numbers. Divisible by 4 but not by 6 = 22 − 8 = 14, giving 14/90 = 7/45. Trap 11/45 = 22/90 forgets the exclusion and reports every multiple of 4. Trap 4/45 = 8/90 reports the excluded multiples of 12 instead. Trap 7/50 = 14/100 counts 100 two-digit numbers, forgetting that they start at 10, not at 0.