Question

There are three different oxygen generation systems onboard the International Space Station (ISS). Assume all three are currently running. System 1 is operational 90% of the time and supports 4 crewmembers. System 2 is operational 60% of the time and supports 6 crewmembers. System 3 is operational 80% of the time and supports 3 crewmembers. In an abnormal event, indicators at Mission Control show that one of the 3 systems has failed. What is the probability that there is an adequate supply of oxygen for a crew of 10.

Answer 1

There will be an adequate supply of oxygen for a crew of 10 only if System 1 and System 2 are operational (Since they support 4 + 6 = 10 crewmembers)

Thus, the failed system should be the System 3

Probability that one of the 3 system has failed

= (0.9*0.6*0.2) + (0.9*0.4*0.8) + (0.1*0.6*0.8) = 0.444

Now, the probability that system 3 failed = 0.9*0.6*0.2 = 0.108

Thus the required probability = 0.108/0.444 = 0.243