question_answer

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

E)  None of these