For a 1:9 ratio, you could simply hook up three randomizers to each other with a 1:3 probability for each. That way the total probability will be 1:3 * 1:3 = 1:9.

He could do so for all numbers under 9 and for all numbers where all prime factors are under 10, so between 1 and 30 he could do:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30.

Math out.