Question
Prove that if E and F are independent events, then so are the events E and F'.
Solution
Since E and F are independent.
∴ P(E ∩ F) = P(E). P(F)
From the Venn diagram in the figure, it is clear that E ∩ F and E ∩ F' are mutually exclusive events and also
∴ E and F' are independent.
Tips: -
Note: In a similar manner, it can be shown that if the events E and F are independent, then
(a) E' and F are independent,
(b) E' and F' are independent.
