One of the twelve months of the year is chosen at random. What is the probability that it has fewer than 31 days?

Five months fall short of 31 days — February, April, June, September and November — so the probability is 5/12. The other seven months have 31 days, giving the complement 7/12. Forgetting February, the shortest month of all, leaves 4/12 = 1/3, and 1/2 assumes long and short months balance, which they do not: the year carries seven long months against five short ones.