1.

Suppose A and B are two independent events with probabilities \({\rm{P}}\left( {\rm{A}} \right) \ne 0\) and \({\rm{P}}\left( {\rm{B}} \right) \ne 0\). Let \({\rm{\bar A}}\) and \({\rm{\bar B}}\) be their complements. Which one of the following statements is False?

A. \({\rm{P}}\left( {{\rm{A}} \cap {\rm{B}}} \right){\rm{\;}} = {\rm{\;P}}\left( {\rm{A}} \right){\rm{P}}\left( {\rm{B}} \right)\)
B. \({\rm{P}}\left( {{\rm{A}}/{\rm{B}}} \right){\rm{\;}} = {\rm{\;P}}\left( {\rm{A}} \right)\)
C. \({\rm{P}}\left( {{\rm{A}} \cup {\rm{B}}} \right){\rm{\;}} = {\rm{\;P}}\left( {\rm{A}} \right){\rm{\;}} + {\rm{\;P}}\left( {\rm{B}} \right)\)
D. \({\rm{P}}\left( {{\rm{\bar A}} \cap {\rm{\bar B}}} \right){\rm{\;}} = {\rm{\;P}}\left( {{\rm{\bar A}}} \right){\rm{P}}\left( {{\rm{\bar B}}} \right)\)
Answer» D. \({\rm{P}}\left( {{\rm{\bar A}} \cap {\rm{\bar B}}} \right){\rm{\;}} = {\rm{\;P}}\left( {{\rm{\bar A}}} \right){\rm{P}}\left( {{\rm{\bar B}}} \right)\)


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