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Expected value question

  1. Feb 6, 2010 #1
    1. The problem statement, all variables and given/known data
    A catalog contains 10 itmes. Two people, A and B each select 3 items from the catalog independently. What is the expected value of the number of items A and B ordered.

    My attempt:
    Let A chose any 3 items. The probability that B
    Chose 1 similar item is 3/10
    Chose 2 of the same items = 3/10*2/9
    Chose 3 of the same items = 3/10*2/9*1/8

    And so the expected value is 1*(3/10) +2*(3/10*2/9) + 3*(3/10*2/9*1/8) = 11/24
    But he awnsers page sais it is 0.9
    I don't really know what I'm doing wrong
    Guidance needed :)
     
  2. jcsd
  3. Feb 6, 2010 #2
    How did you compute your probabilities?
     
    Last edited: Feb 6, 2010
  4. Feb 6, 2010 #3
    A chose any 3 items.
    Then the chance that B chose one of them is 3/10. He has three chances to chose one of ten objects. The chance that B chose 2 of the same is 3/10*2/9 since he had 3 chances for the first one and two chances out of the nine remaining for the next one. etc
     
  5. Feb 6, 2010 #4
    The probability that the first item B chooses is one of A's items is 3/10. But what about the other two? With no restriction, they could be anything: one of A's or not one of A's, coincidental with the first item, etc.
     
  6. Feb 6, 2010 #5
    I don't see why.
    The chance that B took one item is 3/10. Then to chose another item he has two choices left out of 9 other items. So 2/9 and multiply by 3/10 since to get the seconed item he had to get the first item.
     
  7. Feb 6, 2010 #6
    Suppose you want to know the probability that B chooses exactly one of A's items. Then he has to choose one of the 3 items of A, and two of the remaining 7.
     
  8. Feb 6, 2010 #7
    Ok. I got it. Thanks for the help, much apreciated.
    Tal
     
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