Is This Your Card?

A magician randomly draws one card from a standard card deck. The probability that the card drawn is a heart or a diamond can be written as , where  and  are positive, coprime integers. What is the value of ?

Details and assumptions

A standard deck of cards consists of 52 cards, formed by 13 ranks (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q and K) of 4 suits (clubs, diamonds, hearts and spades).