By the end of each academic year, students at the university will have either passed, failed ordeferred the year.Experience has shown that in the Science Faculty :• 88% of students who pass this year will also pass next year• 10% of students who pass this year will fail next year•X% of students who pass this year will defer next year• 52 % of students who fail this year will pass next year• Y% of students who fail this year will fail next year•4% of students who fail this year will defer next year2% of students who defer this year will pass next year10% of students who defer this year wil fail next year• 25 % of students who defer this year will defer next year.Construct a complete transition matrix for this situation, entering the correct values for X, Yand Za.Twelve hundred and thirty students began a Science degree in 2014.By the end of the 2014 academic year, 880 students had passed, 230 had failed, while 120 haddeferred the year.No students have dropped out of the Science degree permanently.b. Use this information to predict the number of Science students who :i.by the end of the 2015 academic year will have deferred the year. i. by the end of the 2016 academic year will have deferred the year.by the end of the 2016 academic year will have passed their third successive yeariii.(and be eligible for graduation).The situation is quite different in the Arts Faculty, where experience has shown :• 75 % of students who pass this year will also pass next year• 15% of students who pass this year will fail next year• 10% of students who pass this year will defer next year• 55 % of students who fail this year will pass next year• 35 % of students who fail this year will fail next year• 10% of students who fail this year will defer next year• 65 % of students who defer this year will pass next year• 15 % of students who defer this year will fail next year• 20 % of students who defer this year will defer next year.Three thousand and ten students began an Arts degree in 2014.By the end of the 2014 academic year, 1980 students had passed, 730 had failed, while 300 haddeferred the year.No students have dropped out of the Art degree permanently.Use this information to predict the number of Art students who :c.i. by the end of the 2016 academic year will have failed the year.ii.by the end of the 2016 academic year will have failed their third successive year(and hence may not be allowed back for 2017).

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