A) \[P(A/B)=\frac{2}{3}\]
B) \[P(A'/B')=\frac{1}{3}\]
C) \[P(A/B')=\frac{1}{3}\]
D) \[P(A/(A\cup B))=\frac{1}{4}\]
Correct Answer: C
Solution :
[c] For option (1) \[P(A/B)=\frac{P(A\cap B)}{P(B)}=P(A)=\frac{1}{3}\] Similarly \[P(A'/B')=P(A')=\frac{2}{3}\] \[P(A/B')=\frac{P(A)(1-P(B))}{(1-P(B))}=\frac{\frac{1}{3}.\frac{5}{6}}{\frac{5}{6}}=\frac{1}{3}\] \[P(A/A\cup B)=\frac{P(A\cap (A\cup B))}{P(A\cup B)}\] \[=\frac{P(A)}{P(A\cup B)}\] \[\frac{\frac{1}{3}}{\frac{1}{3}+\frac{1}{6}-\frac{1}{18}}\] \[=\frac{6}{6+3-1}=\frac{3}{4}\] \[\therefore \] Option (3) is correct
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