There are two bags: the first bag contains 2 red balls and 5 blue balls, while the second one has 3 red balls and 4 blue balls. Someone took a ball from one of these two bags. Assume that each bag has the same chance to be chosen. And within each bag has the same chance to be chose. And within each bag, every ball will be picked up with the same probability. You don't know which bag this ball is from. The only information you know is that the color of this ball is red.

What is the probability that this red ball is from the first bag?

If that person put this ball back to its original bag and pick one ball from the same bag randomly. What is the probability that the second ball is also red?

To make grading easier, let's use the following notation

A1={the first bag chosen}

A2={The second bag is chosen}

B={Pick one ball from one of the two bags and its color is red}

C={Pick a second ball from the same bags as the first time and its color is red}