1. An integrated circuit factory has 3 machines, namely, A, B and C. One integrated circuit...

 

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1. An integrated circuit factory has 3 machines, namely, A, B and C. One integrated circuit produced by each machine is tested, which is either "pass" or "fail", denoted by P or F, respectively. An observation is a sequence of 3 test results corresponding to the circuits from A, B and C. For example, the observed sequence PPF means that the circuits from A and B pass the test while the circuit from C fails the test. (a) Determine the sample space. (b) Determine the elements of the following sets: U = {circuit from C fails} V = {circuit from A passes} X = {more than one circuit pass} Y = {at least two circuits fail} (c) Are U and V mutually exclusive? (d) Are X and Y mutually exclusive? 1. An integrated circuit factory has 3 machines, namely, A, B and C. One integrated circuit produced by each machine is tested, which is either "pass" or "fail", denoted by P or F, respectively. An observation is a sequence of 3 test results corresponding to the circuits from A, B and C. For example, the observed sequence PPF means that the circuits from A and B pass the test while the circuit from C fails the test. (a) Determine the sample space. (b) Determine the elements of the following sets: U = {circuit from C fails} V = {circuit from A passes} X = {more than one circuit pass} Y = {at least two circuits fail} (c) Are U and V mutually exclusive? (d) Are X and Y mutually exclusive?

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a The sample space consists of all possible sequences of test results for the three machines A B and ... View the full answer