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Two Packs Of Cards (Posted on 2004-02-05) Difficulty: 2 of 5
Two identical pack of cards A and B are shuffled throughly. One card is picked from A and shuffled with B. The top card from pack A is turned up.
If this is the Queen of Hearts, what are the chances that the top card in B will be the King of Hearts?

  Submitted by Ravi Raja    
Rating: 3.8571 (7 votes)
Solution: (Hide)
There are two cases to be considered.
CASE 1 : King of Hearts is drawn from Pack A and shuffled with Pack B
Probability of drawing King of Hearts from Pack A = 1/51 (as Queen of Hearts is not to be drawn)
Probability of having King of Hearts on the top of the Pack B = 2/53
So total probability of case 1 = (1/51) * (2/53) = 2 / (51 * 53)
CASE 2 : King of Hearts is not drawn from Pack A
Probability of not drawing King of Hearts from Pack A = 50/51 (as Queen of Hearts is not to be drawn)
Probability of having King of Hearts on the top of the Pack B = 1/53
So total probability of case 2 = (50/51) * (1/53) = 50 / (51 * 53)
Now adding both the probability, the required probability is
= 2 / (51 * 53) + 50 / (51 * 53)
= 52 / (51 * 53)
= 52 / 2703
= 0.0192378

Comments: ( You must be logged in to post comments.)
  Subject Author Date
A KING INDEEDG2004-02-06 20:16:53
Some Thoughtsre(2): Agreement with nobodyPhil2004-02-06 14:42:25
re: Agreement with nobodyCharlie2004-02-06 14:20:34
Some ThoughtsAgreement with nobodyPhil2004-02-06 13:45:34
solutionFreddy Grants2004-02-05 23:48:21
re(4): SolutionPhil2004-02-05 23:28:55
re(3): Solutionwinnifred foster2004-02-05 17:37:36
SolutionAgreement with CharliePhil2004-02-05 15:09:48
Solutionmy solutionAdy TZIDON2004-02-05 13:55:43
re(2): Solutionlovejoy2004-02-05 11:46:33
SolutionBrian Smith2004-02-05 09:09:12
Solutionre: Solutionwinnifred foster2004-02-05 08:45:02
Solutionre: SolutionCharlie2004-02-05 08:43:55
SolutionSolutionstan2004-02-05 08:30:09
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