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Probability of card dealing

 
 
specsol
 
Reply Sun 6 Jan, 2013 12:37 pm
With a randomly shuffled pack of cards how would one calculate the probability of dealing 46 cards and getting 19 of one colour and 26 of the other?
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markr
 
  1  
Reply Sun 6 Jan, 2013 03:58 pm
@specsol,
19+26=45
Are you including jokers as possibilities for the 46th card?
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markr
 
  2  
Reply Sun 6 Jan, 2013 04:11 pm
@specsol,
If you meant 20 of one color and 26 of the other, then:
C(26,20)*C(26,26)*2 / C(52,46) = 0.0226175577

If you meant 19 of one color and 26 of the other (45 cards total), then:
C(26,19)*C(26,26)*2 / C(52,45) = 0.0098337207

C(n,r) = n! / (r! * (n-r)!)
specsol
 
  1  
Reply Mon 7 Jan, 2013 04:47 am
@markr,
many thanks. Yes, I meant 19 of one colour and 26 of the other, obviously mistyped the total!
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