Geometric Probability

Example:

Find the probability that a point chosen at random lies on $\overline{AC}$ .

Probability of the point is on $\overline{AC}=\frac{\text{Length}\text{of}AC}{\text{Length}\text{of}AB}$

Use the Segment Addition Postulate to find the length of $\overline{AB}$

$\begin{array}{l}AB=AC+CB\\ =3+9\\ =12\end{array}$

Substitute.

Probability of the point is on $\overline{AC}=\frac{3}{12}$

$=\frac{1}{4}$

The probability of the point is on $\overline{AC}$ is $=\frac{1}{4}$ or $0.25$ .