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What is the probability of #4

  1. Sep 3, 2011 #1
    What is the probability of the player matching exactly 3 numbers from a 10 number lottery (0...9) w/o repetition, given the conditions:
    - player and lottery pick 6 numbers;
    - player always has a repeated number;
    - lottery always has a repeated number.
    for example:

    123455
    123455

    Here there's many matches of 3. Because it's a match of 6/6 it means that there are C(6,3)=20 matches of 3... I think

    Note. Legit choice:
    123455
    112345
    It also means the player matched 4 numbers while picking only 3, which means C(4,3) ways to match a 3 number... match
     
    Last edited: Sep 3, 2011
  2. jcsd
  3. Sep 7, 2011 #2
    Actually the point is only the number matchings on the lottery using just 3 player numbers.

    This is a conditional probability problem.

    I experimented on matching all numbers between ABCD;EE and ABCD;EE
    Hypothetic (calculated) probability: 1/1260

    Real probability: ~1.75/1260
    0.0013608333 experiment
    0.00138888(8) guess = ~1.75/1260=1/720=1/6!=1/P(10,3)?=1/(1x2x3x4x5x6)

    Anyone knows how to calculate this properly?
     
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