SOLUTION: assuming that geometric distribution on positive integer 1,2,3..find the probability that an integer is even,odd,even when divisible by 3

Look at the first 6 positive integers:

 1,  2,  3,  4,  5,  6.

Which ones are even?:

     2,      4,      6

That's 3 out of 6, so out of the first 6, P(even) = 3/6 = 1/2

Which ones are odd?:

1.      3,      5,     

That's 3 out of 6, so out of the first 6, P(odd) = 3/6 = 1/2

Which one is even when divisible by 3?

                     6,               

That's 1 out of 6, so out of the first 6, P(even when divisible by 3 = 1/6

Now realize that we can say the same thing about the next set of 
6 positive integers:

13, 14, 15, 16, 17, 18

3 out of those 6 are even, 3 out of those 6 are odd, and 1
out of those 6 is even when divisible by 3 (just 18).

It's the same with next 6, and the next 6, etc., etc.

So for the set of ALL positive integers, 

P(even)=1/2, P(odd) = 1/2, P(even when divisible by 3) = 1/6

Edwin