A letter is known to have come either from London or Clifton; on the postmark only the two consecutive letters ON are legible; what is the chance that it came from London?
The Attempt at a Solution
Let us assume that probability that it came from London or Clifton is 1/2. Now the probability that letters ON is selected from London is 2/4 and for Clifton it is 1/6. So the total probability is (1/2 * 2/4 + 1/2 * 1/6). Now the chance that it is from London is (1/2 * 2/4) / (1/2 * 2/4 + 1/2 * 1/6). I can't figure out what's wrong with my solution.