A system is composed of three components A, B, and C. All three must function for the system to function. There are currently no backups in place. The system has a reliability of 0.966. If a backup is installed for component A, the new system reliability will be

A) unchanged.
B) less than 0.966.
C) greater than it would be if a backup were also installed for component B.
D) greater than 0.966.
E) equal to exactly 0.966.

Since all three components are required for the system to function, we can use the multiplication rule of probability to find the reliability of the system if there are no backups:

Reliability(system) = Reliability(A) x Reliability(B) x Reliability(C) = 0.966^3 = 0.904

If a backup is installed for component A, the new reliability of A is 0.992 (assuming the backup has perfect reliability), so the new reliability of the system would be:

Reliability(new system) = Reliability(A backup) x Reliability(B) x Reliability(C) = 0.992 x 0.966^2 = 0.931

Therefore, the new system reliability would be greater than 0.966, which is answer choice D.