by Amaranth
You work out the probability of not drawing one. For four cards, that's:26/30 * 25/29 * 24/28 * 23/27
In order to find the probability of drawing at least one with any arbitrary array of cards, it's (assuming no reshuffles) an equation with z terms. With reshuffles, just assume a 30 card deck, since I think all cards are discarded after you've drawn all cards.
1-((y-x)/y * ((y-1)-x)/(y-1) * ((y-2)-x)/(y-2)...((y-(z-1))-x)/(y-(z-1)))
x = The number of successes remaining in the deck
y = The number of cards remaining in the deck
z = The number of cards you're drawing