In a deck of 52 cards, what is the probability of drawing a card that is not a face card (Jack, Queen, King) or an Ace?

Official Answer

To approach this question, let's first break down the composition of a standard deck of 52 cards. In each of the four suits (hearts, diamonds, clubs, and spades), there are 13 cards. Among these, there are 3 face cards (Jack, Queen, King) and 1 Ace. This gives us a total of 4 cards per suit that we're aiming to exclude from our calculation. Across all four suits, that amounts to 4 cards * 4 suits = 16 cards that we're not interested in drawing.

Now, since there are 52 cards in total and we're excluding 16 specific cards (the face cards and Aces), we're left with 52 - 16 = 36 cards that are neither face cards nor Aces. To find the probability of drawing one of these cards, we simply divide the number of favorable outcomes (drawing a card that is not a face card or an Ace) by the total number of possible outcomes (drawing any card from the deck).

Therefore, the probability of drawing a card that is not a face card or an Ace is 36/52. Simplifying this fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 4. This gives us 9/13.

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