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January 3rd, 2014, 05:28 AM   #1
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Expectation of Drawing Cards of the Same Suit

In the 52 card deck, what is the expected number (average in the long run) of drawings you have to make to get k cards of the same suit, with or without replacement?
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January 3rd, 2014, 11:33 AM   #2
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Re: Expectation of Drawing Cards of the Same Suit

With replacement it is trivially 4k.
Without replacement it is more work to calculate, although for k > 13, it is impossible.
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January 3rd, 2014, 11:54 PM   #3
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Re: Expectation of Drawing Cards of the Same Suit

Nice post!
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January 5th, 2014, 05:52 AM   #4
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Re: Expectation of Drawing Cards of the Same Suit

mathman, why don't you give the solutions, not only the answer.
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January 5th, 2014, 07:36 AM   #5
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Re: Expectation of Drawing Cards of the Same Suit

Quote:
Originally Posted by rubis
mathman, why don't you give the solutions, not only the answer.
Due to cuts duly implemented in 2014, Mathman's position has been made part-time,
thus he does not have enough time, having to drive a taxi in order to make up reduced income...
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January 5th, 2014, 04:08 PM   #6
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Re: Expectation of Drawing Cards of the Same Suit

Quote:
Originally Posted by rubis
mathman, why don't you give the solutions, not only the answer.
If you draw 4k cards (with replacement) you will have on average k cards of each suit.
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