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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: Simulation results | Comment 19 of 36 |
    (In reply to Simulation results by Tony)

    The simulation results tony reports for B seem vastly different from those for A, and suspiciously like what one would expect for the number of cards rather than the number of packets. I ran my own simulation for B (a lot easier than for A, as individual cards can be used until grouped into 5's at the end):
    RANDOMIZE TIMER
    DO
    REDIM c(200)
    ct = 0: ctr = 0
    DO
    r = INT(RND(1) * 200 + 1)
    IF c(r) = 0 THEN
    c(r) = 1
    ct = ct + 1 ' ct must get to 200 each trial
    END IF
    ctr = ctr + 1 ' ctr is number of purchases to complete set
    IF ct = 200 THEN EXIT DO
    LOOP
    tot = tot - INT(-ctr / 5) ' -int(-x) is ceil(x)
    totI = totI + ctr ' individual card count
    numTry = numTry + 1
    PRINT numTry, -INT(-ctr / 5), tot / numTry, totI / numTry
    LOOP

    at trial 8332 the line of output shows
    8332 237 234.8208 1172.123
    The 237 is just the #of packets for that trial, but the average number of packets is 235; the average # of individual cards is 1172.

    Again this is for B, which is easier than A.

      Posted by Charlie on 2003-01-29 10:15:58

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