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.)

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Answer 1

First we find the probability that none of the 4 cards drawn are face cards. There are 40 non-face cards in a standard deck of 52 cards, so the probability that the first person does NOT draw a face card is $\dfrac{40}{52}=\dfrac{10}{13}$. Likewise, the probability that none of the four people draw a face card is $\left(\dfrac{10}{13}\right)^4$. Therefore, the probability that at least one of the four people draws a face card is $1-\left(\dfrac{10}{13}\right)^4\approx \boxed{0.4}$.