You're looking at something like the geometric distribution. The chance that the event does not happen is 88%. And since years are independent and identically

You're looking at something like the geometric distribution. The chance that the event does not happen is 88%. And since years are independent and identically distributed as you say, 88% = q^10 so q~= 98.7%; therefore the chances that it does happen are ~=1.3% (As it turns out, your approximation works because as the time-grid becomes finer and finer, the geometric process becomes a gamma process. It does fail dramatically for 2-7 years.)