There are three odd numbers on a number cube, which are 1, 3, and 5. Since 3 is already an odd number, we don't need to count it twice when finding the probability of rolling an odd number. So, there are a total of four numbers that meet the requirement of being a 3 or an odd number. That means the probability of rolling a 3 or an odd number is 4/6, or 2/3.