Calculate the probability of drawing specific cards from a standard 52-card deck.
Card probability without replacement follows the hypergeometric distribution. The probability of drawing exactly k favorable cards when drawing n cards from a deck of N cards containing K favorable cards is computed using combinations.
P = C(K,k) × C(N−K, n−k) / C(N, n)
1 − P(no aces) = 1 − C(48,5)/C(52,5) ≈ 0.3412 or 34.1%.
Because cards are drawn without replacement, the trials are not independent. The hypergeometric distribution accounts for the changing deck composition.