Anumber is chosen at random from the first 100 positive integers. find the probability that the number is not divisible by 10 or 3

So, possible numbers divisible by 10.
There are 10 of them in the first 100 positive integers.
10, 20, 30, 40, 50, 60, 70, 80, 90, and 100.
And then the ones divisible by 3. There are 33.
3, 6, 9, 12, 15, 18, 21.. you get my point.
However, three of those are shared, 30, 60, and 90. 
So basically add the two together and subtract three for the shared ones. 
10 + 33 - 3 = 40
So there are 40 possibilities, so there is a 4/10 chance that the number is divisible by 10 or 3, so a 6/10 chance that the number is not divisible.
Or 3/5.