Chapter 6.1, Problem 6.11E

A consultant has presented his client with three alternative research studies that could be conducted. If the client chooses alternative a, the consultant will have to hire 1 additional employee. Two new employees will have to be hired if the client chooses b, and 5 if the client chooses c. The probability that the client will select altern ative a is 0.1, with $P(b)=0.5\text{ and }P(c)=0.4$ . Identify the discrete random variable in this situation and determine its expected value.