Question 2 Calculating probability. (a) Two applicants are randomly selected from among five who have applied for a job. Find the probability that exactly one of the two best applicants is selected. (Hint: there are lots of ways to approach this problem. I suggest an approach similar to exercise 2.120 on HW3). (b) Different illnesses may produce the same symptoms. Suppose that a particular set of symp- toms, denoted H, occurs only when one of three illnesses, I, I,, or I; occurs. Assume an individual may only have one of these illnesses at a time and that P(I1) = 0.01, P(12) = 0.02, P(13) = 0.03. Suppose also that the probabilities of developing the set of symptoms H, given each of these illnesses, are known to be P(H I, ) = 0.85, P(H|I2) = 0.90, P(H I3) = 0.95. Assuming that an ill person exhibits the symptoms, H, what is the probability that the person has illness