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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.)
    re(2): a method of solving problem B | Comment 30 of 36 |
    (In reply to re: a method of solving problem B by Charlie)

    This is the program that implements Steve Hutton's algorithm, as modified:
    DEFDBL A-Z
    DIM p(1, 200)' second subscript is # of unique cards gained
    ' first is 0 for old generation (# of cards drawn) and 1 for
    ' next generation of # of cards drawn

    p(0, 1) = 1 ' generation 1 where m = 1
    FOR m = 2 TO 15000
    FOR n = 1 TO m
    IF n > 200 THEN EXIT FOR
    p(1, n) = p(0, n) * n / 200 + p(0, n - 1) * (201 - n) / 200
    p(0, n - 1) = p(1, n - 1)
    NEXT
    p(0, n - 1) = p(1, n - 1)
    s = -INT(-m / 5)
    expVal = expVal + s * (p(1, 200) - prevProb)
    prevProb = p(1, 200)
    NEXT

    PRINT expVal, p(1, 200)
      Posted by Charlie on 2003-02-05 08:57:29

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