MathDB

The

52

cards in a deck are numbered

1, 2, \ldots, 52

. Alex, Blair, Corey, and Dylan each picks a card from the deck without replacement and with each card being equally likely to be picked, The two persons with lower numbered cards from a team, and the two persons 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\plus{}9, and Dylan picks the other of these two cards. The minimum value of

p(a)

for which

p(a)\ge\frac12

can be written as

\frac{m}{n}

. where

m

and

n

are relatively prime positive integers. Find m\plus{}n.

Problem Statement