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Homework Help: Probability question

  1. Jan 24, 2010 #1
    in a room there are 3 married couples
    somebody guesses which of the men are married to which of the women.
    X=number of correct guesses.

    find E(x), var(x)

    i tried the following

    X=0 (no correct guesses)
    P(X)=2/3*2/3*2/3=8/27

    X=1 (one correct guess)
    P(X)=2/3*2/3*1/3=4/27

    X=2 (two correct guesses)
    P(X)=2/3*1/3*1/3=2/27

    X=1 (three correct guesses)
    P(X)=1/3*1/3*1/3=1/27


    BUT the total
    P(X=0) + P(X=1) + P(X=2) + P(X=3) does not come to 1
    (8+4+2+1)/27=5/9

    where am i going wrong? there are only 3 couples so he could not guess more that 3 correct couples.
    the probability of guessing a correct couple is 1 in 3
     
  2. jcsd
  3. Jan 24, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You are assuming the probability of a guess being correct is independent of previous guesses. That's not true. For example, there is no chance at all of getting two guesses correct and the third one wrong.
     
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