If a person draws four cards from a standard deck (without replacing them), what is the probability that at least one of the cards is a face card?

Answer 1

This is the same as making the statement:

Probability(Getting at least 1 Face Card) = 1 - Probability(No face cards)

You have 40 non-face cards, and 12 face cards in a standard deck.

There are ₅₂C₄ options of any 4-card hand in the deck, and ₄₀C₄ options of any hand with no face cards (52 cards - 12 face cards = 40 non-face cards).

So, P[No Face Card] = (₄₀C₄)/(₅₂C₄) = 0.33757

Therefore P[Face Card] = 1 - 0.33757 = .6624 (66.24%)