Dr. Pepper-
3) Years one and fifteen have an average 1.5-year daily window; day one, year one has only until the first day of year two, while the last day of year one has until the last day of year two. The average therefore is 1.5 years.
4) 15 years divided by a two-year window is 7.5. 15 years divided by 1.5 is 10.
5) 13 * 7.5 + 2 * 10 = 117.5. 117.5 / 15 = 7.83. Therefore, the odds of two 100% certainties each of which occurs one within fifteen years both occurring with a year of each other within that fifteen year span is 1/7.83, or about 12.8%.
If you’d said “within the same year”, it would be simply be 1/15 * the odds of both breaking.