perplexus.info :: Probability : Ten not welcomed...

Ten not welcomed... (Posted on 2023-08-30)

The standard 52-card deck will represent a database consisting of 4 identical sets each containing a set of 13 integers: Ace=1, 2 to 10 represent respectively the numerical values, J=11, Q=12 and K=13.
Drawing randomly 2 cards you get two numbers, say n1 and n2. Evaluate the absolute value of d=n1-n2.

What is the probability that d will not be equal to 10?

Please solve analytically and use a simulation program to validate your results.

No Solution Yet Submitted by Ady TZIDON

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No simulations for me (spoiler)

| Comment 1 of 2

d can only = 10 if the n1 is 1,2,3,11,12 or 13. This happens with probability 6/13.

Then, there are only 4 cards out of the remaining 51 that will make d = 10.

So d = 10 with probability (6/13)*(4/51) = 24/663 = 8/221.

So d is not equal to 10 with probability 213/221, which is approximately 96%

Posted by Steve Herman on 2023-08-30 08:46:30

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