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) 74% get a positive recommendation (event R). However, out of those candidates that are not eligible 73% get a negative recommendation. Overall, they know that only 13% of all job applicants are actually eligible.
    What is the corresponding fourfold table of the joint probabilities? (Specify all entries in percent.)
      R    R   sum
      E   %   %   % 
      E    %   %   % 
    sum  %   %   % 


    Solution

    Using the information from the text, we can directly calculate the following joint probabilities:
    P(ER) = P(R|E)·P(E)=0.74·0.13=0.0962=9.62% P( E R ) = P( R | E )·P( E )=0.73·0.87=0.6351=63.51%.

    The remaining probabilities can then be found by calculating sums and differences in the fourfold table:
      R    R   sum
      E   9.62   3.38   13.00 
      E    23.49   63.51   87.00 
    sum  33.11   66.89   100.00 

    1. P(ER)=9.62%
    2. P( E R)=23.49%
    3. P(E R )=3.38%
    4. P( E R )=63.51%
    5. P(R)=33.11%
    6. P( R )=66.89%
    7. P(E)=13.00%
    8. P( E )=87.00%
    9. P(Ω)=100.00%