The odds that an American is of English ancestry are 1:9. What is the probability that an American is of English ancestry?

There are 36 possible outcomes of the additive dice roll. The way to roll a sum of 9 is 6 (and vice versa) and 3 or 5 and 4 (and vice versa). This is possible 4 of the 36 times, giving a probability the sum of the two dice rolled of 4/36 or 1/9.

If the odds are 1:9 than the probability is:

1 - 1/9 = 8/9

100 / 9 * 1 = 11.111 ... ⇒ 11.11 %