A) \[\frac{3}{4}\]
B) \[\frac{5}{6}\]
C) \[\frac{1}{4}\]
D) \[\frac{3}{7}\]
Correct Answer: C
Solution :
\[P(A)=1-0.3=0.7\] \[P(B)=0.4\] \[P(A\cap \overline{B})=0.5\Rightarrow P(A)-P(A\cap B)=0.5\] \[\Rightarrow \]\[P(A\cap B)=0.2\] Now, \[P\left( \frac{B}{A\cup \overline{B}} \right)=\frac{P(B\cap (A\cup \overline{B}))}{P(A\cup \overline{B})}\] \[=\frac{P\left( (B\cap A)\cup (B\cap \overline{B}) \right)}{P(A)+P(\overline{B})-P(A\cap \overline{B})}\] \[=\frac{P(B\cap A)}{P(A)+P(\overline{B})-P(A\cap \overline{B})}=\frac{0.2}{0.8}=\frac{1}{4}\]You need to login to perform this action.
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