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 machine 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: Z_F = {circuit from Z fails} X_A = {circuit from X is acceptable}
(c) Are Z_F and X_A mutually exclusive? (Explain)
(d) Are Z_F and X_A collectively exhaustive? (Explain)
(e) What are the elements of the sets: C = {more than one circuit is acceptable} D = {at least two circuits fail}
(f) Are C and D mutually exclusive? (Explain)
(g) Are C and D collectively exhaustive? (Explain)