Question 8 [4 marks] If in a certain university the principal governs poorly, the probability of remaining in that position for the next six years is 5%. If the same principal is deemed to govern satisfactorily the probability of remaining in that position for the next six years is 2T%. If the principal's governance is adjudged to be well, the probability of remaining in that position for the next six years is 58% whereas if the principal governs excellently, the probability of remaining in that position for the next six years is 90%. A survey revealed that 13% of the stakeholders of the company rated the principal as governing poorly, 39% of the said stakeholders rated the principal as being satisfactory, 37% rated the principal as governing well and only 1 1% rated the principal's governing as being excellent. i. Given that the principal of the university remains in the position for the next six years, what is the probability that the principal governed satisfactorily? [2] ii. Draw the Probability Tree that represents the given scenario. [2]