probability question

Question

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. (c) 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

Answer 1

Since the highest probability of hiring someone can be = 1, we can have the highest value of the set {x, 2x, 4x} to be equal to one. The highest value in this set is 4x. So

4x <=1

Hence x<=1/4

This should be the answer.

Now the situation would be harder if the company has a limit on the hires it could make (this is not the question, though). If you have any related questions, feel free to message me on my profile!