Question 882198
*[Tex \Large \overline{A}] is the complementary event of event A. It is the complete opposite of event A. So that means


*[Tex \Large P(A) + P(\overline{A}) = 1]


since one or the other event must happen (but not both at the same time). Isolate *[Tex \Large P(\overline{A})] to get


*[Tex \Large P(\overline{A}) = 1 - P(A)]


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Now plug in the given probability P(A) = 0.4 and evaluate



*[Tex \Large P(\overline{A}) = 1 - P(A)]


*[Tex \Large P(\overline{A}) = 1 - 0.4]


*[Tex \Large {\color{black} P ( \overline{A} ) } = {\color{red}0.6}]