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. Four additional people do the same. Find the probability that of the 5 cards drawn, at least 1 is a face card. (Round your answer to one decimal place.)

Question

Mathematics

Houston Noble

27 April, 20:58

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. Four additional people do the same. Find the probability that of the 5 cards drawn, at least 1 is a face card. (Round your answer to one decimal place.)

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Answers (1)

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Graham Duke · Answer 1

Step-by-step explanation:

There are 12 face cards (4 kings, 4 queens, and 4 jacks).

That means 40 cards are not face cards.

The probability that at least 1 of the 5 cards drawn is a face card is equal to 1 minus the probability that all of the cards were not face cards.

P (at least 1) = 1 - P (no face cards)

P = 1 - (40/52) ⁵

P = 0.731

The probability is 73.1%.