A Machine Has Four Components $A , B , C$ , and D, Set Up in Such a Manner That

Multiple Choice

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 $P ( \mathrm {~A} ) = P ( \mathrm {~B} ) = 0.97 , P ( \mathrm { C } ) = 0.9$ , and $P ( \mathrm { D } ) = 0.94$ . Find the probability that the machine works properly.

A) $0.8206$
B) $0.204$
C) $0.796$
D) $0.8468$