SOLUTION: A standard deck of 52 playing cards consists of four different suits
and 13 cards of different ranks in each suit. Four cards will be drawn at
random without replacement from thi
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-> SOLUTION: A standard deck of 52 playing cards consists of four different suits
and 13 cards of different ranks in each suit. Four cards will be drawn at
random without replacement from thi
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Question 261184: A standard deck of 52 playing cards consists of four different suits
and 13 cards of different ranks in each suit. Four cards will be drawn at
random without replacement from this deck. The probability that the
four cards will be all the same suit is k times the probability that they
will be all the same rank. What is the value of k?
You can put this solution on YOUR website! A standard deck of 52 playing cards consists of four different suits
and 13 cards of different ranks in each suit. Four cards will be drawn at
random without replacement from this deck. The probability that the
four cards will be all the same suit is k times the probability that they
will be all the same rank. What is the value of k?
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P(all cards same suit) = [4*13C4]/[52C4]
P(all cards same rank) = [13*4C4]/52C4 = 13/52C4
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Equation:
P(same suit) = k*P(same rank)
Note: the denominators cancel; you end up with:
[4*13C4] = k*13
k = (4/13)(13C4)
k = 220
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Cheers,
Stan H.
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