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45-733 PROBABILITY AND STATISTICS I


Answer to Problem 2



Let A1 = Urn I, A2 = Urn II,
  1. B = Yellow Ball is Drawn, Bc = Green or Red Ball is Drawn

    A Diagram of this is:

    P(A1) = P(A2) = 1/2
    P(B | A1) = 16/30
    P(B | A2) = 10/30
    Hence:

    P(A2|B) = [P(A2)P(B|A2)]/ [åj=1,2 P(Aj)P(B|Aj)] =
    
                             1 10
                             -*--
                             2 30       5
             P(A2 | B) = ----------- = --
                         1 16   1 10   13
                         -*-- + -*--
                         2 30   2 30
    


  2. B = Red Ball is Drawn, Bc = Yellow or Green Ball is Drawn

    A Diagram of this is:

    P(A1) = P(A2) = 1/2
    P(B | A1) = 2/30
    P(B | A2) = 8/30
    Hence:

    P(A1|B) = [P(A1)P(B|A1)]/ [åj=1,2 P(Aj)P(B|Aj)] =
    
                             1  2
                             -*--
                             2 30      1
             P(A1 | B) = ----------- = -
                         1  2   1  8   5
                         -*-- + -*--
                         2 30   2 30