In a musical chair game,the person playing the music has been advised to stop playing the music at any time within $2 \, \text{minutes}$ after she starts playing. What is the probability that the music will stop within the first half-minute after starting?

(1/4) Here,the possible outcomes are all the numbers between $0$ and $2$. This is the portion of the number line from $0$ to $2$.
Let $E$ be the event that 'the music is stopped within the first half-minute'.
The outcomes favourable to $E$ are points on the number line from $0$ to $\frac{1}{2}$.
The total distance from $0$ to $2$ is $2$,while the distance favourable to $E$ from $0$ to $\frac{1}{2}$ is $\frac{1}{2}$.
Since all the outcomes are equally likely,we can argue that,of the total distance of $2$,the distance favourable to the event $E$ is $\frac{1}{2}$.
So,$P(E) = \frac{\text{Distance favourable to the event } E}{\text{Total distance in which outcomes can lie}} = \frac{\frac{1}{2}}{2} = \frac{1}{4}$.