Let A, B, C be three mutually independent events. Consider the tw… - Vidyadip

MCQ

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

✓
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

Correct option: A.

Both ${S_1}$ and ${S_2}$ are true

a
(a) $B \cup C$ is independent to $A,$ so ${S_1}$ is true

$B \cap C$ is also independent to $A,$ so ${S_2}$ is true.

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