Answer
$\dfrac{2}{3}$ or, $66.7 \%$
Work Step by Step
The probability that the point $T$ lies on the segment $\overline{QT}$ can be computed as:
$\text{P(point on $\overline{QT})$}=\dfrac{QT}{ST}$
$\dfrac{SQ}{QT}=\dfrac{1}{2}$
Let us suppose that $SQ=x\implies QT=2x$. Also, $ST=x+2x=3x$
Therefore,
$\text{P(point on $\overline{QT})$}=\dfrac{2x}{3x}=\dfrac{2}{3}$ or, $66.7 \%$
