In the musical-chair timing model shown on the number line in Fig. 14.1, the music may stop at any time from 0 to 2 minutes, all instants being equally likely. What is the probability that it stops within the first half-minute? 

When outcomes are points on a line segment, probability is found using length ratio. The total possible interval is from 0 to 2 minutes, so total length is 2. The favourable interval is from 0 to $\frac{1}{2}$ minute, so its length is $\frac{1}{2}$. Hence $P(E)=\frac{\frac{1}{2}}{2}=\frac{1}{4}$.