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(A) Given that, $P(A)=\frac{1}{3}$, $P(A \cap B)=\frac{1}{5}$, $P(A \cup B)=\frac{3}{5}$.We know that, $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Subst

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(A) Given that, $P(A)=\frac{1}{3}$, $P(A \cap B)=\frac{1}{5}$, $P(A \cup B)=\frac{3}{5}$.We know that, $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.Substituting the values: $\frac{3}{5} = \frac{1}{3} + P(B) - \frac{1}{5}$.$P(B) = \frac{3}{5} + \frac{1}{5} - \frac{1}{3} = \frac{9+3-5}{15} = \frac{7}{15}$.Now, matching the items:$A$. $P(\frac{A}{B}) = \frac{P(A \cap B)}{P(B)} = \frac{1/5}{7/15} = \frac{3}{7}$ (Matches $(v)$).$B$. $P(\bar{B}) = 1 - P(B) = 1 - \frac{7}{15} = \frac{8}{15}$ (Matches $(iii)$).$C$. $P(A \cap \bar{B}) = P(A) - P(A \cap B) = \frac{1}{3} - \frac{1}{5} = \frac{2}{15}$ (Matches $(i)$).$D$. $P(B \cap \bar{A}) = P(B) - P(A \cap B) = \frac{7}{15} - \frac{1}{5} = \frac{4}{15}$ (Matches $(ii)$).Thus, the correct matching is: $A-(v), B-(iii), C-(i), D-(ii)$.

List-$I$	List-$II$
$A$. $P(\frac{A}{B})$	$(i)$. $\frac{2}{15}$
$B$. $P(\bar{B})$	$(ii)$. $\frac{4}{15}$
$C$. $P(A \cap \bar{B})$	$(iii)$. $\frac{8}{15}$
$D$. $P(B \cap \bar{A})$	$(iv)$. $\frac{2}{3}$
	$(v)$. $\frac{3}{7}$

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