A magician shuffles a standard deck of playing cards and allows an audience member to pull out a card, look at it, and replace it in the deck. Three additional people do the same. Find the probability that of the 4 cards drawn, at least 1 is a face card. (Round your answer to one decimal place.)
There are 12 face cards in a standard deck of 52 playing cards (3 face cards in each of the 4 suits). The probability of not drawing a face card in a single draw is the complement of drawing a face card, which is:
P(not a face card) = (52 - 12)/52 = 40/52 = 20/26 = 10/13.
To find the probability that none of the 4 cards drawn are face cards, we multiply the probabilities of not drawing a face card in each of the 4 draws:
P(all 4 not face cards) = (10/13)^4 ≈ 0.038.
Finally, to find the probability that at least 1 of the 4 cards drawn is a face card, we take the complement of P(all 4 not face cards):
P(at least 1 face card) = 1 - P(all 4 not face cards) ≈ 1 - 0.038 ≈ 0.962.
Therefore, the probability that at least 1 of the 4 cards drawn is a face card is approximately 96.2%.