Problem:
Jenn randomly chooses a number from . Bela then randomly chooses a number from distinct from . The value of is at least with a probability that can be expressed in the form where and are relatively prime positive integers. Find .
Solution:
There are equally likely pairs . In 19 of those pairs , , the numbers differ by less than 2 , so the probability that the numbers differ by at least 2 is . Then holds in exactly half of these cases, so it has probability . The requested sum is .
The problems on this page are the property of the MAA's American Mathematics Competitions