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3 votes
3 votes
Two cards are drawn together from a pack of 52 cards, What is the probability that One is spade and other is king??

3 Answers

Best answer
5 votes
5 votes
case 1 spade king and spade or non-spade king and spade (1/52 x 12/51  +3/52  x 13/51)=51/52 x51=1/52

case 2  spade x non spade king or spade and spade king (13/51 x 3/51    +  12/51 x 1/52) =51/52x51=1/52

total prob =1/52+1/52 =1/26 ans
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2 votes
2 votes
Total sample space = 52C2

No. of  spade = 13

No. of king = 4

so probability = (13 * 4 ) / 52C2
edited by
1 votes
1 votes
With Replacement:

$\frac{_{1}^{13}\textrm{C} *_{1}^{4}\textrm{C} }{_{1}^{52}\textrm{C} *_{1}^{52}\textrm{C} }$

Without Replacement:

$\frac{(_{1}^{1}\textrm{C} *_{1}^{3}\textrm{C})+(_{1}^{12}\textrm{C}*_{1}^{4}\textrm{C})) }{_{2}^{52}\textrm{C}  }$
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