Statement-1 : If A and B are two events such that P(A)=1, then A and B are independent.
Statement-2: A and B are two independent events iff
`P(A cap B)=P(A)P(B)`

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Answer

A

Explanation

Clearly, statement -2 is true. (See theory) .
If P , ` P (A) =1 " then " P( overline AP =0`
Now, ` overline A cap B sub overline A`
` Rightarrow P ( overline cap b) le P ( overlineA) `
` Rightarrow P ( overlineA cap b) le 0`
` Rightarrow P ( overlineA cap B) =0`
` Rightarrow P ( overline cap B) =P ( overline A) P (B)`
` Rightarrow overlineA and B` are independent events.
` Rightarrow A and B ` are indepdent event.