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