perplexus.info :: Probability : Card Shuffle Conclusion

Card Shuffle Conclusion (Posted on 2022-05-20)

(I) Three identical packs of cards A, B and C, each being standard 52 card decks, are shuffled thoroughly. One card is picked from A and shuffled with B. Again, one card is picked from B and shuffled with C. Finally, one card is picked from C and shuffled with A.
The top card from A is now turned up and found to be the Jack of Hearts.
Determine the probability that the respective top cards in B and C will be the Queen of Hearts and the King of Hearts (in this order.)

(II) With all the other conditions of the problem remaining the same, suppose:
The top cards from A and B are turned up and are respectively found to be the Jack of Hearts and the Queen of Hearts.
Determine the probability that the top card from C will be the King of Hearts.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

(Part 1) The required probability is:
36557/98741968 ~= 0.000370227581447435
(Part 2) The required probability is:
36557/1899586 ~= 0.0192447196389108
For an explanation, refer to the solution submitted by Charlie in this location.

Comments: ( You must be logged in to post comments.)

	Subject	Author	Date
	computer-aided solution	Charlie	2022-05-20 14:01:31

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