Suppose that Box I contains 6 red balls and 9 green balls, and Box II contains 8 red balls and 12 green balls. All the balls of Box I and Box II are mixed together and a ball is chosen at random from them. Let $$E_1$$ be the event that the ball chosen belonged to Box I and let $$E_2$$ be the event that the ball chosen belonged to Box II. Let $$F_1$$ be the event that the ball chosen is red and let $$F_2$$ be the event that the ball chosen is green.

Then which of the following statements is (are) TRUE?