A housie ticket number is drawn at random from the numbers 1 to 90. What is the probability that the number drawn contains the digit 7?

Numbers ending in 7 are 7, 17, 27, 37, 47, 57, 67, 77 and 87 — nine of them — and numbers in the seventies are 70 to 79, another ten. But 77 belongs to both lists, so the count is 9 + 10 − 1 = 18 and the probability is 18/90 = 1/5. Adding the two lists without removing the repeat gives 19/90; counting only the numbers that END in 7 gives 9/90 = 1/10; and 2/9 = 20/90 comes from claiming ten numbers in each list, which quietly admits 07 as a number in the range.