We have two urns, where urn-1 contains 3 blue balls and 1 red ball while urn-2 contains 2 blue balls and 2 red balls. Suppose we will randomly select one of the two urns, and then randomly pick a ball from the selected urn.
a) What is the probability that we will pick a blue ball?
b) If we picked a blue ball, what is the probability that the selected urn was urn-1?
c) Suppose we picked a blue ball. If we randomly pick one additional ball from the same urn, what is the probability that we pick a red ball?