Please answer the following question and give the explanations. Thanks

Problem 1 (20p). In this question we draw balls from urns. (a) (10p) An urn contains 4 red balls labelled 1, 6 red balls labelled 0, and 6 white balls labelled 1. How many white balls labelled 0 must be in the urn for the events of a certain colour drawn or a certain label drawn to be independent when a ball is drawn uniformly at random from the urn? (b) (10p) Urn A contains 5 red and 7 blue balls. Urn B contains 3 red and 12 blue balls. We flip a fair coin. If the coin lands tails, then a ball is drawn from urn A. If the coin lands heads, then a ball is drawn from urn B. Suppose that a red ball is selected. What is the probability that the coin landed heads? Your answers do not have to include an explicit probability model, and you should arrive at your final answer without using a calculator