The probability of the sum of two balanced dice being a multiple of 3 or greater than 4 is 9/36 or 1/4 (option OD. 9).
When two balanced dice are rolled, there are 36 possible outcomes. To find the probability of the sum being a multiple of 3 or greater than 4, we count the favorable outcomes. There are 9 favorable outcomes: 2 outcomes with a sum of 3 and 7 outcomes with sums greater than 4. Dividing the favorable outcomes (9) by the total outcomes (36), we get a probability of 1/4. Therefore, the correct option is OD. 9.