One of the solar instruments on a satellite has three major parts which must all operate.Two have reliabilities of .7,and the other has a reliability of .9.In case the system fails,there is an identical backup system which kicks on automatically.The overall reliability of the system,including the backup,is closest to:
A) .40
B) .50
C) .60
D) .70
E) .80

Question

Quizplus · Accepted Answer

To calculate the overall reliability of the system, we need to use the formula:

Overall Reliability = 1 - [(1 - R1) x (1 - R2) x (1 - R3)]

where R1, R2, and R3 are the reliabilities of the three major parts.

Plugging in the values, we get:

Overall Reliability = 1 - [(1 - 0.7) x (1 - 0.7) x (1 - 0.9)]
= 1 - [0.3 x 0.3 x 0.1]
= 0.91

Since there is an identical backup system, the overall reliability is increased to 0.91. Therefore, the closest answer choice is D) .70.

One of the Solar Instruments on a Satellite Has Three