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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.)
    Hints/Tips re: Another analytic solution to problem B | Comment 32 of 36 |
    (In reply to Another analytic solution to problem B by Rick)

    It's not a bug in Excel. The same total comes up in a Basic program to evaluate that sum. I'm sure the difference is in the not counting of higher number of cards resulting from full packs having to be chosen. But that doesn't happen often enough to round to the next integer of packs, 236. In fact, notice that, carried to more decimal places, your total is 235.1212379248, while the version counting full packs produces 235.5212379248, which differ by exactly .4 packs (due to rounding differences, decimals after this differ). When you think about it, the least extra cards you might need to fill out a pack is zero, and the most is four. That averages to two, which is .4 packs.
      Posted by Charlie on 2003-02-06 05:55:44

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