A) \[\frac{2}{5}\]
B) \[\frac{4}{5}\]
C) \[\frac{6}{5}\]
D) \[\frac{7}{5}\]
Correct Answer: C
Solution :
\[P(A\cup B)=\frac{3}{4}\] Now, \[P(A\cap B)=\frac{1}{5}\] \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\] \[\Rightarrow \] \[P(A)+P(B)=P(A\cup B)+P(A\cap B)\] \[\Rightarrow \] \[P(A)+P(B)=\frac{3}{5}+\frac{1}{5}=\frac{4}{5}\] \[\Rightarrow \] \[1-P(\overline{A})+1-P(\overline{B})=\frac{4}{5}\] \[\Rightarrow \] \[-\{P(\overline{A})+P(\overline{B})\}=\frac{4}{5}-2=\frac{-6}{5}\] \[\Rightarrow \] \[P(\overline{A})+P(\overline{B})=\frac{6}{5}\]
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