There are 3 bags each containing 100 marbles. Bag 1 has 75 red and 25 blue marbles. Bag 2 has 60 red and 40 blue marbles. Bag 3 has 45 red and 55 blue marbles. Now a bag is chosen at random and a marble is also picked at random.
1) What is the probability that the marble is blue?
2) What happens when the ﬁrst bag is chosen with probability 0.5 and other bags with equal probability each?
I understand the #1, I got .4 but how would I approach doing #2?