Answer Happy

(20 pts.) The Research & Development Department of a manufacturing company classifies the past projects as follows: full success (45% of the population), partial success (35%) and failure (20%). Sixteen past projects were randomly selected to identify factors attributing the outcome of the projects. a) (4 pts.) At least three of each class should be selected. What is the probability that exactly 5 fully successful projects will be selected and that partially successful projects will outnumber the failed projects? b) (2 pts.) In the selection process for the sixteen projects, what is the probability that the last project selected is the 4th partially successful project in the group? c) (2 pts.) In the selection process for the sixteen projects, what is the probability that the last project selected is the 1st failed project in the group? d) (4 pts.) Answer the question in letter (a) if it is known that the department has a total past project of only 100. e) (4 pts. If it is known that the department has a total project of 20 per year, what is the probability that three of the last five years will have at 6 to 12 fully successful projects? 0 (4 pts. Assume that projects failed due to the following reasons: lacking in budget, lacking in time, and lacking in expertise. The department found out that 0.9% of the total failed projects was due to the lack of expertise. What is the probability that there will be at most three failed projects from 150 failed projects was due to lack of expertise?