A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are $P ( \mathrm {~A} ) = P ( \mathrm {~B} ) = 0.91 , P ( \mathrm { C } ) = 0.94 , \text { and } P ( \mathrm { D } ) = 0.93$ . Find the probability that the machine works properly.
A) 0.7955
B) 0.7784
C) 0.2761
D) 0.7239

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The Answer of A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are $P ( \mathrm {~A} ) = P ( \mathrm {~B} ) = 0.91 , P ( \mathrm { C } ) = 0.94 , \text { and } P ( \mathrm { D } ) = 0.93$ . Find the probability that the machine works properly.
A) 0.7955
B) 0.7784
C) 0.2761
D) 0.7239

A Machine Has Four Components, A, B, C, and D P( A)=P( B)=0.91,P(C)=0.94, and P(D)=0.93P ( \mathrm {~A} ) = P ( \mathrm {~B} ) = 0.91 , P ( \mathrm { C } ) = 0.94 , \text { and } P ( \mathrm { D } ) = 0.93P( A)=P( B)=0.91,P(C)=0.94, and P(D)=0.93

A Machine Has Four Components, A, B, C, and D $P ( \mathrm {~A} ) = P ( \mathrm {~B} ) = 0.91 , P ( \mathrm { C } ) = 0.94 , \text { and } P ( \mathrm { D } ) = 0.93$