Question: A purchasing unit for a state government has found that 70% of the winning bids for office-cleaning contracts come from regular bidders, 20% from occasional

A purchasing unit for a state government has found that 70% of the winning bids for office-cleaning contracts come from regular bidders, 20% from occasional bidders, and 10% from first-time bidders. The services provided by successful bidders are rated satisfactory or unsatisfactory after one year on the job. Experience indicates that 80% of the jobs done by regular bidders are satisfactory, as are 70% of the jobs done by occasional bidders and 50% of the jobs done by first-time bidders.

(1) What is the probability of the event A: "a job will be done by a regular bidder"?

(2) What is the probability of the event B: "a job will be satisfactory"?

(3) Are the events A and B independent? Why or why not?

(4) Are the events A and B mutually exclusive? Why or why not?

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