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 Three of a Kind (Posted on 2003-11-19)
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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 When is there gonna be a solution? | Comment 38 of 39 |
I just don't know if I can take the suspense anymore!!!!!!

Anyway here is my \$.02. Im very new at this.

The probability of getting three of a kind for n number of draw is:

P(n)=((3*(n-1))/(52-(n-1))*((2*(n-1))/52-(n-1))

For n>2 and where n is the number of draws.

Using this formula I got that at 16th draw you have a 0.986 probility of getting three of a kind.

in the case of 2 decks I came to a 0.986 probabiltiy of having three of a kind on 31 draws. (substitue 104 for 52)

Edited on December 31, 2003, 4:52 pm
 Posted by snapp on 2003-12-31 16:01:50

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