A) \[\frac{9}{10}\]
B) \[\frac{8}{10}\]
C) \[\frac{7}{10}\]
D) \[\frac{3}{5}\]
Correct Answer: C
Solution :
Given,\[P(\bar{A}\cup \bar{B})=P(\overline{A\cap B})=\frac{7}{10}\] Since,\[P(A\cap B)+P(\overline{A\cap B})=1\] \[\Rightarrow \] \[P(A\cap B)=1-\frac{7}{10}=\frac{3}{10}\] Also, \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\] \[\Rightarrow \] \[\frac{4}{5}=P(A)+\frac{2}{5}-\frac{3}{10}\] \[\Rightarrow \] \[P(A)=\frac{4}{5}-\frac{2}{5}+\frac{3}{10}\] \[=\frac{2}{5}+\frac{3}{10}=\frac{7}{10}\]You need to login to perform this action.
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