7. A computer manufacturing firm produces three product lines: (1) desktop computer systems, (2) notebook computers, and (3) subnotebook computers. The sales department has convened its monthly meeting in which the four staff members of the department provide the department manager with their indications of whether sales will increase for each of the product lines in the coming month. Let Ai represent the event that sales for product line i (¼1, 2, or 3) will increase in the coming month. The manager will consider the information of a given staff member to be usable if that information is internally consistent, where internally consistent in this context means consistent with the axioms and theorems of probability. Which of the staff members have provided the manager with usable information? Be sure to provide a convincing reason if you decide that a staff member’s information needs to be discarded.

Staff member Tom Dick Harry Sally P(A1) .5 .3 .3 .2 P(A2) .3 .2 .6 .3 P(A3) .7 .8 .4 .5 P(A1\A2) .9 .4 .4 .2 P(A1\A3) .6 .15 .2 .3 P(A2\A3) .15 .1 .1 .4 P(A1\A2\A3) .1 1.5 .05 .1