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 Question from maribie, a student: a standard deck of playing cards contains 26 black cards and 26 red cards, or 52 cards in all. a deck is randomly divided into two unequal piles, such that the probability of drawing a red card from the small pile is 1/3. at the same time, the probability of drawing a black card from the larger pile is 5/14. how many cards are in the larger pile?

Maribie,

Suppose the number of cards in the larger pile is $x$ then the number of cards in the smaller pile is $52 - x.$ Since the probability of rawing a red card from the smaller pile is 1/3, one-hird of the cards in the smaller pile are red. Hence the number of red cards in the smaller pile is $\frac13 \times (52 - x).$

What is the probability of drawing a red card from the larger pile? What is the number of red cards in the larger pile? The sum of the number of red cards in the smaller pile and the number of red cards in the larger pile is $26.$ Solve for $x.$

Penny

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