A wooden die used in a board game is not an ordinary one: its six faces carry the numbers 1, 1, 2, 3, 3 and 5. It is rolled twice and the two numbers are added. What is the probability that the total is 4?

The six faces are still equally likely, so the two rolls give $6\times 6=36$ equally likely outcomes — but the numbers repeat, so each total must be counted face by face. A total of 4 comes from 1 then 3, which can happen in $2\times 2=4$ ways because either 1-face may pair with either 3-face; from 3 then 1, another 4 ways; and from 2 then 2, just 1 way. That is 9 outcomes, so the probability is 9/36 = 1/4. On an ordinary die a total of 4 arises in only 3 ways, giving 1/12 — the answer for the wrong die. Overlooking the 2 and 2 case leaves 8/36 = 2/9, and counting only one order of 1 and 3 leaves 4/36 = 1/9.