One bag contains 4 white balls and 6 black balls. Another bag contains 8 white balls and 2 black balls. A coin is tossed to select a bag, then a ball is randomly selected from that bag. What is the probability that a white ball will be drawn?

Suppose a white ball was drawn. What is the probability that it came from the first bag? Suppose there is a 70% chance that the first bag is selected. How would the probabilities change?