Each of the 12 ordered boxes contains 12 coins, consisting of pennies and dimes. The number of dimes in each box is equal to its order among the boxes, that is, box number 1 contains one dime and 11 pennies, box number 2 contains two dimes and 10 pennies, etc. A pair of fair dice is tossed, and the total showing indicates which box is chosen to have a coin selected at random from it.
(a) Find the probability that a coin selected is a dime.
(b) It is observed that the selected coin is a penny. Find the probability that it came from box number 4.