If I have a randomly selected integer between 0000 and 9999, what is the probability that the digit sum of that number is divisible by 5?
[E.g. 1234 = 1 + 2 + 3 + 4 = 10]
I've started off with knowing that I have 2 options for the last integer, but I'm not sure where to go from there.
Best Answer
Hint: Pick the first three digits randomly first, and then focus on the last one.
It's similar to how the probability of getting the sum $7$ when throwing two dice can be seen to be $\frac16$ by noting that no matter what the first die shows, the result on the second die can make the sum $7$ in exactly one way.