To find the probability that the sum of the numbers rolled is odd or greater than 10, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Let's break it down:
1. Odd sum: The possible outcomes for an odd sum are (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (3, 6), (4, 1), (4, 3), (4, 5), (5, 2), (5, 4), (5, 6), (6, 1), (6, 3), (6, 5). There are 18 favorable outcomes.
2. Sum greater than 10: The possible outcomes for a sum greater than 10 are (5, 6), (6, 5), (6, 6). There are 3 favorable outcomes.
Now, let's calculate the total number of possible outcomes. Since each cube has 6 sides, there are 6 possible outcomes for each cube. Since we are rolling two cubes simultaneously, the total number of possible outcomes is 6 * 6 = 36.
To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)
Probability = (18 + 3) / 36
Probability = 21 / 36
The probability that the sum of the numbers rolled is odd or greater than 10 is 21/36, which can be simplified to 7/12.