4. In the following problem, choice “at random” means equally likely among the alternatives.

Suppose there are three boxes, A, B and C, each of which contains two coins. Box A has two pennies, Box B one penny and one nickel, and Box C two nickels. A box is chosen at random, and then a coin is chosen at random from that box. The coin chosen turns out to be a nickel. What is the probability that the other coin in the chosen box is also a nickel? Show each step in your argument.