Answer
$\dfrac{3}{7}$ or, $42.9 \%$
Work Step by Step
The probability that the point $T$ lies on the segment $\overline{BC}$ can be computed as:
$P(T \in \overline{BC})=\dfrac{BC}{AD}$
Where, $BD=9-6=3$ and $AD=10-3=7$
Now, $P(T \in \overline{BC})=\dfrac{BC}{AD}=\dfrac{3}{7}$ or, $42.9 \%$