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 ) get a positive recommendation (event ). However, out of those candidates that are not eligible get a negative recommendation. Overall, they know that only of all job applicants are actually eligible.
What is the corresponding fourfold table of the joint probabilities? (Specify all entries in percent.)
Using the information from the text, we can directly calculate the following joint probabilities: The remaining probabilities can then be found by calculating sums and differences in the fourfold table: