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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.)
    Some Thoughts attempt at case B | Comment 11 of 39 |
    1st pack: you get an average of 3 diff. cards. 197 more to go to complete the series.

    a pack may have all same - all different , each withy prob. 1/5.

    u may get 0 - 5 new cards per pack , but since cards may repeat in a pack , these probs are weighted.

    average # of new cards per pack =
    (1*1 + 2*4/5 + 3*3/5 + 4*2/5 + 5*1/5 )/6 = 7/6.

    to complete 197 new cards , 197/7/6 = 197*6/7 = 169 approx.

    total # of packs = 169 + 1 = 170
      Posted by Keedom on 2002-11-19 00:26:36
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