A snowboard manufacturer has three plants, one in the eastern United States, one in the western United States, and one in Canada. Production records show that the U.S. plants each produced 10,000 snowboards last month, while the Canadian plant produced 8000 boards. Of all the boards manufactured in Canada last month, 4% had a defect that caused the boards to delaminate prematurely. Records kept at the U.S. plants show that 3% of the boards manufactured in the eastern United States and 6% of the boards manufactured in the western United States had this defect as well.
a. What proportion of the boards manufactured last month were defective?
b. What is the probability that a snowboard is defective and was manufactured in Canada?
c. Given that a snowboard is defective, what is the probability that it was manufactured in the United States?
Let D denote the event that a snowboard is defective, let ? denote the event that a snowboard is made in the eastern United States, let W denote the event that a snowboard is made in the western United States, and let C denote the event that a snowboard is made in Canada. Then P(E) = P(W) = 10/28, P(C) = 8/28, P(D|E) = 3/100, P(D|W) = 6/100, and P(D|C) = 4/100.
(a) 
(b) 
(c) Let U be the event that a snowboard was made in the United States.
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