Let's break it down:

Number of favorable outcomes (odd numbers): There are three odd numbers on a six-sided dice, which are 1, 3, and 5.

Number of favorable outcomes (numbers less than 4): There are three numbers less than 4 on a six-sided dice, which are 1, 2, and 3.

However, we need to be careful not to count the number 1 twice since it satisfies both conditions (odd and less than 4).

So, the total number of favorable outcomes is 3 + 2 - 1 = 4.

Total number of possible outcomes: Since we are rolling a fair six-sided dice, there are six possible outcomes (numbers 1 to 6).

Now, we can calculate the probability:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes) Probability = 4 / 6 Probability = 2 / 3

Therefore, the probability of getting an odd number or a number less than 4 when rolling a fair six-sided dice is 2/3