Bag 1 contains 6 red balls. 7 blue balls, and 3 green balls.
Bag 2 contains 8 red balls, 8 blue balls, and 2 green balls.
Bag 3 contains 2 red balls. 9 blue balls, and 8 green balls.
Bag 4 contains 4 red balls. 7 blue balls, and no green balls.
Bag 1 is chosen with a probability of 0.15, bag 2 with a probability of 0.20, bag 3 with a probability of 0.35, and bag 4 with a probability of 0.30, and then a ball is chosen at random from the bag. Calculate the probabilities:
(a) A blue ball is chosen
(b) Bag 4 was chosen if the ball is green
(c) Bag 1 was chosen if the ball is blue