A box initially contains four balls, three of which are black and one white. At each stage a ball is randomly selected from the box and replaced with a new ball. If the ball that is selected is black, it is replaced with a black ball with probability 0.7, and replaced with a white ball with probability 0.3. If the ball that is selected is white, it is replaced with a white ball with probability 0.6 and a black one with probability 0.4. Find the probability that the fourth ball selected is white.