A system is composed of two parts which must both operate in order for the system to perform as intended.The parts have reliabilities of .6 and .5.There is an identical backup system connected to the main system by a switch which has a reliability of .9.The probability that the overall system will operate is closest to:
A) .30
B) .40
C) .50
D) .60
E) .70

Question

Quizplus · Accepted Answer

The overall system will operate if either the main system and backup system both operate or the switch connects the backup system to the main system when the main system fails. We can calculate the probability using the following formula:

P(overall system operates) = P(both systems operate) + P(main system fails) * P(backup system operates) * P(switch connects)

= (0.6*0.5) + (0.4*0.5*0.9)

= 0.3 + 0.18

= 0.48

Therefore, the closest probability is .50, which is answer choice C).

A System Is Composed of Two Parts Which Must Both