Question

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

• A. $1$
• B. $\frac{1}{2}$
• C. $\frac{1}{8}$
• D. $\frac{1}{4}$

Answer 1

The correct option is D $\frac{1}{4}$

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 the points on the number line from 0 to 1/2.
The distance from 0 to 2 is 2, while the distance from 0 to $\frac{1}{2}$ is $\frac{1}{2}$.
Since all the outcomes are equally likely, and out of the total distance of 2, the distance favourable to the event E is 1/2. So,
$PE=\frac{DistancefavourabletotheeventE}{Totaldistanceinwhichtheoutcomecanlie}=\frac{1/2}{2}=\frac{1}{4}$