a six sided dicen numbered 1-6 is rolled. What's the probability that the roll results in an odd number or a number less than 4?

This is a not mutually exclusive case.

How many odd numbers are on a die? 1,3,5

3 of them.

How many numbers less than 4? 1,2,3

3 of them.

So far we have 3/6+3/6=1/2+1/2.

But we have to subtract off the odds less than 4, otherwise, we double count.

How many odds less than 4? 1,3

2/6=1/3

So, we have 1/2+1/2-1/3 is the probability of drawing an odd or a number less than 4.