What is the probability that a positive integer chosen at random

- is even?
- is odd?
- is divisible by 3?
- leaves a remainder of 1 if you divide it by 3?
- is divisible by both 3 and 5?
- is divisible by both 2 and 6?
- is not divisible by 3?
- is divisible by neither 3 nor 5?

Explain your answers.

Another problem:

Find a way to generate a string of 1000 consecutive numbers, none
of which are prime.