Answer:
The answer is 5/8.
I saw an answer that gave 3/32, and since I knew that was wrong I wanted to give my answer to not lead others astray.
Explanation:
There are 8 numbers john can pick.
Numbers less than 4 are (1, 2, 3)
Numbers that are a multiple of 4 are (4, 8)
The word "or" in the question implies addition, and adding 3/8 and 2/8 yields a result of 5/8. This is also the answer in the test that I took.