There are two bags A and B, each containing 4 cards with the numbers $1,2,3,4$ written on them. Person 甲 draws two cards from bag A, and person 乙 draws two cards from bag B, each randomly. The probability that the sum of the numbers on the two cards held by 甲 equals the sum of the numbers on the two cards held by 乙 is $\frac { q } { p }$. Find the value of $p + q$.\\
(Here, $p , q$ are coprime natural numbers.) [4 points]