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Trading cards (Posted on 2002-05-03) Difficulty: 3 of 5
A trading card series has 200 different cards in it, which are sold in 5-card packages.

Each package has a random sampling of the cards (assume that any card of the 200 has an equal chance of being in a package).

On the average, how many packages will need to be bought to collect the complete series if...

  • A: all the cards in a package will always be different
  • B: a package can have repeats

  • See The Solution Submitted by levik    
    Rating: 4.1818 (11 votes)

    Comments: ( Back to comment list | You must be logged in to post comments.)
    its more complicated | Comment 2 of 39 |
    Ok, heres my idea im not sure of it though but anyway..

    your chance of getting a new card for every card in the first pack is 1, you can't have any doubles.

    For the 2nd pack chance of getting a new card:
    1st card: 195/200
    2nd card: 194/199
    3rd card: 193/198
    4th card: 192/197
    5th card: 191/196

    Now for the 3rd pack
    1st card: 190/200
    2nd card: 189/199
    3rd card: 187/198
    4th card: 186/197
    5th card: 185/196

    And so on until you reach the end

    I think this idea might be the right solution but i have no idea of how to do the maths needed to figure it out, i think levik is some sorta maths fan, im pretty sure it'd involve series but thats as much as i can figure out of it.
      Posted by Eamon on 2002-05-10 00:01:49
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