ACT Math · Probability and counting

A standard deck of 52 cards is shuffled, and one card is drawn. What is the probability of drawing a face card (jack, queen, or king)?

A standard deck of 52 cards is shuffled, and one card is drawn. What is the probability of drawing a face card (jack, queen, or king)?

Answer and explanation

Answer: B: 3/13

The face cards are the jacks, queens, and kings. There are 33 of them in each of the 44 suits, so there are 1212 face cards in a deck of 5252. The probability is 1252=313\frac{12}{52}=\frac{3}{13}, choice B. Choice A (352\frac{3}{52}) counts the face cards in only one suit. Choice C (413\frac{4}{13}) is the probability of drawing a specific rank-type group of 1616 cards, such as counting the aces as well. Choice D (14\frac{1}{4}) is the probability of drawing a card from a particular suit. Count carefully which cards qualify.

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