A printer has five book binding machines. For each machine, the table below gives the proportion of the total book produc that it binds and the probability that the machine produces defective binding: Proportion of Books Bound 20% Probability of Defective Binding 3% 2% Machine Machine 1 Machine 2 10% 2% 4% Machine 3 30% Machine 4 10% Machine 5 30% 1% For instance, Machine 1 binds 20% of ALL books and produces a defective binding with probability of 0.03-3%. Suppose that one of the books is selected at random. (a) What is the probability that this random book was bound by Machine 1? (b) What is the probability that this random book has defective binding? om hook was hound by Machine 1 AND has defective binding?

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A printer has five book binding machines. For each machine, the table below gives the proportion of the total book production
that it binds and the probability that the machine produces defective binding:
Probability of
Defective Binding
3%
2%
2%
Proportion of
Books Bound
Machine
Machine 1
20%
Machine 2
10%
30%
10%
Machine 3
4%
Machine 4
Machine 5
30%
1%
For instance, Machine 1 binds 20% of ALL books and produces a defective binding with probability of 0.03=3%.
Suppose that one of the books is selected at random.
(a) What is the probability that this random book was bound by Machine 1?
(b) What is the probability that this random book has defective binding?
(c) What is the probability that this random book was bound by Machine 1 AND has defective binding?
(d) If you KNOW that the book was bound by Machine 1, what is the probability that it has defective binding?
(e) If you KNOW that the book has defective binding, what is the probability that it was bound by Machine 1?
Transcribed Image Text:A printer has five book binding machines. For each machine, the table below gives the proportion of the total book production that it binds and the probability that the machine produces defective binding: Probability of Defective Binding 3% 2% 2% Proportion of Books Bound Machine Machine 1 20% Machine 2 10% 30% 10% Machine 3 4% Machine 4 Machine 5 30% 1% For instance, Machine 1 binds 20% of ALL books and produces a defective binding with probability of 0.03=3%. Suppose that one of the books is selected at random. (a) What is the probability that this random book was bound by Machine 1? (b) What is the probability that this random book has defective binding? (c) What is the probability that this random book was bound by Machine 1 AND has defective binding? (d) If you KNOW that the book was bound by Machine 1, what is the probability that it has defective binding? (e) If you KNOW that the book has defective binding, what is the probability that it was bound by Machine 1?
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