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Mathematics, 22.02.2021 19:10 igotdiss2178

An integrated circuit factory has three machines X, Y, and Z. Test one integrated circuit produced by each machine. Either a circuit is acceptable (a) or it fails (f). An observation is a sequence of three test results corresponding to the circuits for machines X, Y, and Z, respectively. For example, aaf is the observation that the circuits from X and Y pass the test and the circuit from Z fails the test. a. What are the elements of the sample space of this experiment?
b. What are the elements of the sets:

ZF={circuit from Z fails},
XA ={circuit from X is acceptable}.

c. Are ZF and XA mutually exclusive?
d. Are ZF and XA collectively exhaustive?
e. What are the elements of the sets C={more than one circuit acceptable}, D={at least two circuits fail}.
f. Are C and D mutually exclusive?
g. Are C and D collectively exhaustive?

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