Pressurized air are being used in a manufacturing company in its daily operation

Question

Pressurized air are being used in a manufacturing company in its daily operation. There are three compressors in service; two-screw type compressors, (S1 ,S2) and one-reciprocal type compressor,(R). Each compressor, at any given time, is either off (0), or on (1) . Assume that event A is denoted to reciprocal compressor (R) that is always off . Event B is denoted that at least one of the screw type of compressor is always on. Assume that all outcomes in event event B are equaly likely. If P(AB)=45% and P(AB)=93%. Compute the probability that all compressors are off?

Explanation / Answer

The probability that all compressors are off=P(A)

=P(AB)+P(AcBc)

=0.45+(1-0.93)

=0.52

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