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Independence problem

  1. Oct 15, 2011 #1
    A server sends 3 digits (0 and 1) to a computer. The probability of sending 0 is p.
    I have to check under which conditions the events:

    A={at least 2 of 3 digits is 0}
    B={all the digits are the same}

    are independent.

    I thought that they will be independent if the first 2 digits are different with each other.
    e.g (0,1,0) or (1,0,0)

    But i am not sure for that answer.
    Can you tell me your ideas?
     
  2. jcsd
  3. Oct 15, 2011 #2
    If they are independent then P(AB) = P(A) P(B).
    So to solve:
    1. Determine a formula for P(AB) as a function of p
    2. Determine a formula for P(A) P(B) as a function of p
    3. Set them equal, and solve for p
     
  4. Oct 15, 2011 #3
    thank you mXSCNT for your help.

    So after calculations I found that p=1 or p=1/2.
    Can you confirm that this is the right answer?
     
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