All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Probability
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.)
    my result | Comment 6 of 39 |
    (oops i fked up before pressing
    spacebar when the post button
    was in focus :)

    define

    E to be the expectation of
    different cards in 5 card package

    f(x) to be the average increase
    in distinct cards when the person
    already has x and buys another package

    C(x) to be the average number
    of distinct cards after x
    packages

    then

    C(0) = 0
    C(n) = C(n-1) + f(C(n-1))
    f(x) = E*(200 - n) / 200

    the only difference between
    case A and B is E, the rest is
    the same

    E(A) = 5
    E(B) = 4.95 (to 3 dec. places)

    the answer is to find
    n such that C(n) = 200

    i dont think this can be done
    analitically. numerically
    however the answer is

    A n = 237
    B n = 240
      Posted by Cheradenine on 2002-06-11 08:22:50
    Please log in:
    Login:
    Password:
    Remember me:
    Sign up! | Forgot password


    Search:
    Search body:
    Forums (0)
    Newest Problems
    Random Problem
    FAQ | About This Site
    Site Statistics
    New Comments (8)
    Unsolved Problems
    Top Rated Problems
    This month's top
    Most Commented On

    Chatterbox:
    Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information