Question

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

• A. Both $S _ { 1 }$ and $S _ { 2 }$ are true
• B. Only $S _ { 1 }$ is true
• C. Only $S _ { 2 }$ is true
• D. Neither $S _ { 1 }$ nor $S _ { 2 }$ is true

Answer 1

Answer: (A)

Both $S _ { 1 }$ and $S _ { 2 }$ are true

Answer 2

$B \cup C$ is independent to $A$, so $S _ { 1 }$ is true

$B \cap C$ is also independent to $A$, so $S _ { 2 }$ is true.