Three bottles of different sizes contain different compositions of red and blue candy. The largest bottle contains eight red and
two blue pieces, the mid-size bottle has five red and seven blue, the small bottle holds four red and two blue. A monkey will pick one of these three bottles, and then pick one piece of candy from it. Because of the size differences, there is a probability of 0.5 that the large bottle will be picked, and a probability of 0.4 that the mid-size bottle is chosen. Once a bottle is picked, it is equally likely that the monkey will select any of the candy inside, regardless of color. a. What is the probability that a blue candy is picked?
b. If a blue candy is picked, what is the probability that the large bottle was selected?
