Exam 1

  1. Question

    An industry-leading company seeks a qualified candidate for a management position. A management consultancy carries out an assessment center which concludes in making a positive or negative recommendation for each candidate: From previous assessments they know that of those candidates that are actually eligible for the position (event E) 66% get a positive recommendation (event R). However, out of those candidates that are not eligible 65% get a negative recommendation. Overall, they know that only 9% of all job applicants are actually eligible.
    What is the corresponding fourfold table of the joint probabilities? (Specify all entries in percent.)

    1. P(ER)
    2. P( E R)
    3. P(E R )
    4. P( E R )


    Using the information from the text, we can directly calculate the following joint probabilities:
    P(ER) = P(R|E)·P(E)=0.66·0.09=0.0594=5.94% P( E R ) = P( R | E )·P( E )=0.65·0.91=0.5915=59.15%.

    The remaining probabilities can then be found by calculating sums and differences in the fourfold table:
      R    R   sum
      E   5.94   3.06   9.00 
      E    31.85   59.15   91.00 
    sum  37.79   62.21   100.00 

    1. P(ER)=5.94%
    2. P( E R)=31.85%
    3. P(E R )=3.06%
    4. P( E R )=59.15%