1. The general manager of the Hilton Hotel in Sydney isevaluating an employment screening test for the front officeclerical staff. During this evaluation all new clerical employeesare given the test. 70% pass the test; the rest fail. At a latertime, after the new clerical employees have been working for awhile, their performance is evaluated as being satisfactory orunsatisfactory. Historically, 80% of all clerical employees havebeen found to be satisfactory, and 75% of the satisfactory clericalemployees in the evaluation of the employment screening test havepassed the screening test. (a) From the given information,determine the probabilities of the following events: (i) passingthe test, (ii) having satisfactory performance and (iii) passingthe test given satisfactory performance. [3 marks] (b) Using youranswers to part (a), determine the probability of a clericalemployee passing the test and having satisfactory performance. [1mark] (c) Using your answer in parts (a) and (b), determine theprobabilities of the a clerical employee: (i) failing the test andhaving satisfactory performance, (ii) failing the test and havingunsatisfactory performance, (iii) passing the test and havingunsatisfactory performance, and (iv) having unsatisfactoryperformance. [4 marks] (d) Using your answers in part (c),determine the probabilities of a clerical employee: (i) failing thetest given they are found to have unsatisfactory performance, (ii)failing the test given they are found to have satisfactoryperformance, (iii) passing the test given they are found to haveunsatisfactory performance, (iv) unsatisfactory performance giventhey failed the test, (v) satisfactory performance given theypassed the test, (vi) unsatisfactory performance given they passedthe test, and (vii) satisfactory performance given they failed thetest. [7 marks] (e) Using your answers in part (d), determine thefollowing percentages: (i) clerical employees who failed the testand prove to be unsatisfactory, and (ii) clerical employees whopassed the test and who prove to be satisfactory. [2 marks] (f)Government guidelines require screening tests to achieve at least20% for part (i) in (e) and at least 60% for part (ii) in (e). Doesthis test meet those government requirements? Explain. [2marks]