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Events $A$, $B$ and $C$ occur with respective probabilities $0.52$, $0.13$ and $0.07$. Event $A$ is independent of the events $B$ and $C$. Event $A$ is also independent of the joint occurrence of $B$ and $C$. If the probability of the event $B \cap C$ is $0.03$, compute the probability of the event $B \cap C \cap A$.

I tried to solve it: \begin{align*} \Pr(B \cap C \cap A) & = \Pr(B \cap C)\Pr(A)\\ & = 0.03 \cdot 0.52\\ & = 0.0156 \end{align*}

Is it correct? If not, then please tell me the correct answer or at least tell me the final answer to check by myself.

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It is correct.

$A$ and $B \cap C$ are independent, so $P(A\cap B \cap C) = P(A) P(B \cap C) = 0.03 \times 0.52 = 0.0156$.

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