Solution Found!
A snowboard manufacturer has three plants, one in the
Chapter 2, Problem 13SE(choose chapter or problem)
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?
Questions & Answers
QUESTION:
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?
ANSWER:
Solution 13SE
Step1 of 3:
We have A snowboard manufacturer has three plants, one in the eastern United States, one in the western United States, and one in Canada.
Let us consider D denote the event that a snowboard is defective.
Let E 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.
The number of plants produced by eastern U.S. = 10000
The number of plants produced by western U.S. = 10000
The number of plants produced by Canada = 8000
Hence, the total number of plants produced by U.S. and Canada = 10000+10000+8000
= 28000.
Canada has 4% defect that caused the boards to delaminate prematurely = 4/100.
Eastern U.S.has 3% defect that caused the boards to delaminate prematurely = 3/100.
Eastern U.S.has 6% defect that caused the boards to delaminate prematurely = 6/100.
We need to find,
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?
Step2 of 3:
P(E) =
=
=
P(W) =