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Dr. Ali Moshtagh Probability Problems

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1 Dr. Ali Moshtagh Probability Problems
9/22/2018

2 The Michigan Molding Co.
The Michigan Molding Co. produces two-color legend plates for aircraft cockpits using four machines ( W, X, Y, and Z ). After quality-control inspection, the plates are graded as A, acceptable; B, needs repair; and C, can be scrapped. 1 9/22/2018

3 A sample of 1,000 legend plates revealed the following results:
2

4 State in symbols, the probability that a legend plate selected at random
was produced by machine W. was produced by machine X and needs repair. Needs repair given that it was produced by machine Y. (restricted to plates produced by machine W) is acceptable. was either produced by machine Z or can be scrapped. 3

5 State in words the meaning of each of the following
P ( B | Z ) P ( A  Y ) P ( B U X ) 4

6 Compute the probability that a plate selected at random
was produced by machine Z. was produced by machine X and is acceptable. is acceptable, given that it was produced by machine X. is either in need of repair or was produced by machine W. 5

7 Use the addition theorem or multiplication theorem, as appropriate, to compute the following probabilities P ( Y  B ) P ( C U X ) P ( A  C ) 6

8 Determine if the variables (machine and grade) are statistically independent and show why or why not. 7


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