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Three of a Kind (Posted on 2003-11-19) Difficulty: 4 of 5
You have a standard pack of 52 playing cards. You then shuffle them and begin to draw out cards until you have three of a kind. What is the most likely number of cards drawn when this happens?

You then shuffle another pack of 52 playing cards into the pile. What happens to the expected number of cards now? (i.e. does it double / halve / stay the same?)

No Solution Yet Submitted by Lewis    
Rating: 4.3333 (9 votes)

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Just a thought.. | Comment 20 of 39 |
I may be thinking about this all wrong.. but hear me out.

If u have a deck of cards and u draw out one card at a time. according to odds, wouldnt the most likely situation be that if u drew out 13 cards, the cards that you would have would be 2-A?

I mean the probability of pairing up is less likely than getting a card in which there are four others rather than three..

Using this (absurd) logic, wouldnt that mean that the likelyhood of getting a three of a kind would most likely come exactly between 26(number of cards drawn before u can no longer not have a pair) and 39(the number of cards drawn before u can no longer have 3 of a kind)

...i know this is very wrong, and i know its wrong because it was too easy to think of.. but according to what i said, the average number of cards would be (39-26) / 2 = 6.5 + 26 = 32.5

Could someone explain how this is incorrect. even though im almost positive it is.
  Posted by Chris on 2003-11-20 15:30:51
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