2010 AIME II Problem 13

The 52 cards in a deck are numbered 1, 2, \cdots, 52. Alex, Blair, Corey, and Dylan each pick a card from the deck randomly and without replacement. The two people with lower numbered cards form a team, and the two people with higher numbered cards form another team. Let p(a) be the probability that Alex and Dylan are on the same team, given that Alex picks one of the cards a and a+9, and Dylan picks the other of these two cards. The minimum value of p(a) for which p(a)\ge\frac{1}{2} can be written as \frac{m}{n}, where m and n are relatively prime positive integers. Find m+n.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.