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GO Classes DA Test Series | Artificial Intelligence | Topic Wise Test 2 | Question: 11

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Which of the follwing expressions is/are equivalent to $\mathbf{P}(\mathbf{A}, \mathbf{B} \mid \mathbf{C})$, given that $\mathbf{A} \perp \mathbf{B} \mid \mathbf{C}$ ? NOTE : $X \perp Y \mid Z$ means $X$ is independent of $Y$ given $Z$.
  1. $\frac{P(C \mid A) P(A \mid B) P(B)}{P(C)}$
  2. $\frac{P(B, C \mid A) P(A)}{P(B, C)}$
  3. $\frac{P(A \mid C) P(B, C)}{P(C)}$
  4. $P(A \mid B, C) P(B \mid C)$

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