Question

Find the probability that the entire system works properly. The primary air exchange system on a proposed spacecraft has four separate components (call them A,B,C,D) that all must work properly for the system to operate well. Assume that the probability of any one component working is independent of the other components. It has been shown that the probabilties of each component working are P(A)=0.95, P(B)=0.90, P(C)=0.99 and P(D)=0.90.

Answer 1

The system will work properly when all the 4 components work properly.

So, the probability that all the components work properly =

Probability that components A works properly *

Probability that components B works properly *

Probability that components C works properly *

Probability that components D works properly *

= 0.95 * 0.90 * 0.99 * 0.90

= 0.761805

So, the probability that the entire system works properly is 0.761805.

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