(Similar to Ghahramani Section 3.4, Problems 6, 8, and 14) Threeblack boxes are labeled with Roman numerals I, II and III.
• Box I contains four red chips and three blue chips.
• Box II contains two red chips and five blue chips.
• Box III contains seven red chips and no blue chips. Solve eachof the following problems.
(a) Suppose a box is selected at random and three chips aredrawn at random from the box. If all three chips are red, what isthe probability they were drawn from Box I?
(b) Suppose one chip is selected at random from each box. If twoof the three chips drawn are red chips, what is the probabilitythat the chip drawn from Box II was red?
(c) Suppose three chips are randomly selected from Box I andplaced in Box III. If a chip subsequently drawn randomly from BoxIII is blue, what is the probability that all three chips movedfrom Box I to Box III were blue.
