Drawing from a deck of cards.

Suppose there is a deck consisting of 54 cards (standard deck with one black and one red joker). A single card is drawn from the deck of 54 cards but is not returned to the deck, and then a second card is drawn. Determine the probability of drawing:

1) the red joker or a red ace on either draw

I first thought it would be the probability of the first plus the probability of the second minus the intersection, but that was not the case.

The answer in the book is 1 - (50/53 * 51/54) = 52/477

Can anyone explain how they got their answer? Thanks!