Question 215650: YOU DRAW 2 CARDS FROM A STANDARD DECK WITHOUT REPLACEMENT. DETERMINE THE PROBABILITY THAT:
A. BOTH ARE DIAMONDS
B. NEITHER IS A DIAMOND
C. BOTH ARE OF THE SAME SUIT
D. BOTH ARE OF THE SAME SUIT, GIVEN THAT THE FIRST DRAWN IN A CLUB
E. THEY ARE NOT OF THE SAME SUIT
F. THEY ARE NOT OF THE SAME SUIT, GIVEN THAT THE FIRST DRAWN IN A CLUB.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! YOU DRAW 2 CARDS FROM A STANDARD DECK WITHOUT REPLACEMENT. DETERMINE THE PROBABILITY THAT:
A. P(BOTH ARE DIAMONDS) = 13C2/52C2 = 78/1326 = 0.0588...
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B. EITHER IS A DIAMOND = 1 - 0.0588 = 0.9412
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C. BOTH ARE OF THE SAME SUIT = 4*0.0588 = 0.2353
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D. BOTH ARE OF THE SAME SUIT, GIVEN THAT THE FIRST DRAWN IN A CLUB
P(C|C| = (13/52) * (12/51) = 0.0588...
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E. THEY ARE NOT OF THE SAME SUIT = 1 - 0.0588 = 0.9412..
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F. THEY ARE NOT OF THE SAME SUIT, GIVEN THAT THE FIRST DRAWN IS A CLUB.
P(not club|Club) = 12/51*13/52 = 0.0588
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Cheers,
Stan H.
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