If A and B are events such that P(A | B)=P(B | A), then - Vidyadip

MCQ

If $A$ and $B$ are events such that $P(A | B)=P(B | A),$ then

A
$A \subset B$ but $A \neq B$
B
$A=B$
C
$P(A)=P(B)$
D
$A \cap B=\phi$

✓

Answer

It is given that, $\mathrm{P}(\mathrm{A} / \mathrm{B})=\mathrm{P}(\mathrm{B} | \mathrm{A})$

$\Rightarrow \frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{B})}=\frac{\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{P(A)}$

$\Rightarrow \mathrm{P}(\mathrm{A})=\mathrm{P}(\mathrm{B})$

Thus, the correct answer is $C$.

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