JEE Advance - Mathematics (1994 - No. 8)
Let $$A, B, C$$ be three mutually independent events. Consider the two statements $${S_1}$$ and $${S_2}$$
$${S_1}\,:\,A$$ and $$B \cup C$$ are independent
$${S_2}\,:\,A$$ and $$B \cap C$$ are independent
Then,
$${S_1}\,:\,A$$ and $$B \cup C$$ are independent
$${S_2}\,:\,A$$ and $$B \cap C$$ are independent
Then,
Both $${S_1}$$ and $${S_2}$$ are true
Only $${S_1}$$ is true
Only $${S_2}$$ is true
Neither $${S_1}$$ nor $${S_2}$$ is true