0.125 mg.
Explanation
The mass of a radioactive species decrease by [tex]\dfrac{1}{2}[/tex] by the end of each half-life.
For this 1.00 mg sample of unknown half-life:
Mass of the sample at the end of the n-th half-life;
[tex]\begin{array}{ll} \text{n} & \text{Mass} \; (\text{mg})\\1 & 1.00 \times \dfrac{1}{2} = 0.500\\2 & 1.00 \times {\dfrac{1}{2}}^{2} = 0.250 \\3 & 1.00 \times {\dfrac{1}{2}}^{3} = 0.125\\\dots & \dots \end{array}[/tex].
As a result,
[tex]1.00 \times {\dfrac{1}{2}}^{3} = 0.125 \; \text{mg}[/tex]
of the sample remains after three half-lives.
