Bag A contains balls numbered 2, 4, 4, 4.
Bag B contains balls numbered 1, 1, 2, 3, 4, 4.
Bag C contains balls numbered 1, 2, 3, 4.
One of these three bags is chosen at random.
A ball is chosen at random from this bag.
Find the probability that the ball chosen is numbered 4.
Give your answer as a fraction.