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mixer [17]
3 years ago
7

ou find a deck of cards and know that the deck has too many clubs and spades in it. The deck has 59 cards. If you were to draw t

wo cards without replacement, the probability of drawing a diamond and a club is 117 1711 . How many extra spades are in the deck?
Mathematics
1 answer:
sashaice [31]3 years ago
7 0
We can find the number of extra clubs in the deck from the given probability, since the probability of drawing a diamond and a club is

\dfrac{\binom{13}1\binom{13+c}1}{\binom{59}2}=\dfrac{13(13+c)}{1711}

but this would imply that c=-4, which suggests we're taking 4 clubs out of the original deck and contradicts the problem statement that there are "too many clubs".

Perhaps the question is providing the probability of drawing a diamond, THEN a club, or vice versa. In that case, we have

\dfrac{\binom{13}1}{\binom{59}1}\cdot\dfrac{\binom{13+c}1}{\binom{58}1}=\dfrac{13(13+c)}{3422}

and solving gives c=5, which makes more sense. Then the number of extra spades in the deck must be 2.
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