Quant Interview Practice Questions

Suppose you are analyzing the performance of two algorithmic trading strategies, A and B, on days when the VIX index is above 20. Let C be the event that the VIX index is above 20 on a given day. You observe that strategies A and B's returns are conditionally independent given C. Specifically, let A be the event that strategy A is profitable on a given day, and let B be the event that strategy B is profitable on the same day. You are told that $P(A \cap B | C) = P(A | C) P(B | C)$. Does this c