Rachel, Sam and Thomas applied for a common position at the company. Only one of them will be hired for the position. The probabilities that each of them is hired for the role are given by 17/12/17/1 The probabilities that Rachel, Sam and Thomas can help boost the company's revenue are given by - and respectively, if they are hired. 4 1 3 5'2 10 (a) (b) and respectively. (c) Find the probability that Thomas is selected for the position given that the company's revenue did not improve. (5 marks) Find the probability, p, that the company's revenue will generally improve. (4 marks) Rachel, Sam and Thomas interviewed at another company for another position. The probabilities that each of them is hired for the role are now given by x, 2x and 4x respectively. It can be assumed that the hiring process for each individual candidate are independent of one another. Suppose there is no limit to the number of hires the company can make (i.e. the company can hire any one of them, any two of them, all three of them or no one at all). Find an inequality that must satisfied by x.