A bag contains 5 white and 3 black balls, a second bag contains 4 white and 5 black balls, a third bag contains 3 white and 6 black balls. A bag is selected at rendom and a ball is drawn. Find the probability that the ball is black.
Do the problem assuming that the probability of choosing the first bag is twice as much as choosing the second bag, which is twice as much as choosing the third bag.