[Math] the probability that a randomly chosen positive three-digit integer is a multiple of $7$

Question

What is the probability that a randomly chosen positive
three-digit integer is a multiple of $7$?

Is my answer right?:

$$\frac{100}{7} = 14 , \qquad \frac{999}{7} = 142$$

Then there are $142 – 14 = 128$ numbers that are multiples of $7$.

Then the probability is: $\frac{128}{900}$.

Answer 1

Yes, except that:

1. I would replace $\frac{100}{7}$ with $\frac{99}{7}$ (to see why this is important consider the analogous question asking for how many multiples of $7$ there are in $\{700, \ldots, 999\}$), and
2. the quotients aren't quite right as written, but we can repair them with floor notation, e.g., $\lfloor\frac{999}{7}\rfloor = 142$.