please answer a) and b), please write down on the paper.
Suppose that there are four coins, among them, a bad coin with weigh different from the others. (a) How many weightings are necessary (i.e. the minimal number of weightings in the worst case) using a pan balance to determine which of the four coins is the bad one and the bad coin is heavier/lighter than the others. (b) Draw a decision tree that has the minimal number of weightings in the worst case