Q: Bag 1: 3 red, 2 blue. Bag 2: 1 red, 4 blue. A bag is picked at random, then a ball drawn. Find P(red). P(Bag1) = P(Bag2) = 1/2. P(red) = P(Bag1)P(red|Bag1) + P(Bag2)P(red|Bag2). = (1/2)(3/5) + (1/2)(1/5) = 3/10 + 1/10 = 4/10 = 2/5.