JEE Advance - Mathematics (1989 - No. 2)
If $$E$$ and $$F$$ are independent events such that $$0 < P\left( E \right) < 1$$ and $$0 < P\left( F \right) < 1,$$ then
$$E$$ and $$F$$ are mutually exclusive
$$E$$ and $${F^c}$$ (the complement of the event $$F$$) are independent
$${E^c}$$ and $${F^c}$$ are independent
$$P\left( {E|F} \right) + P\left( {{E^c}|F} \right) = 1.$$