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 from 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?