There are 100 boxes, and for each i = 1, 2, . .. 100, box i contains proportion I /100 of gold coins (the rest are silver), one box is chosen at random, then a coin is drawn at random from this box.

a) If the coin drawn is gold, which box would you guess was chosen? Why?

b) Suppose the boxes were not picked at random, but according to the following scheme. All the even-numbered boxes are equally likely, all the odd-numbered boxes are equally likely, but the chance of drawing an odd numbered box is twice the chance of drawing an even-numbered box, if the coin drawn is good, which box would you guess was chosen? [Hint: write down the prior odds.]