(Q3) 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 she starts playing. What is the probability that the music will stop within the first half-minute after starting?

Solution :

Here the possible outcomes are all the numbers between 0 and 2. This is the portion of the number line from 0 to 2.

2100.5

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
1
2
The distance from 0 to 2 is 2, while the distance from 0 to
1
2
 is
1
2
Since all the outcomes are equally likely, we can argue that, of the total distance is and the distance favourable to the event E is
1
2
  P(E) =
Distance favourable to the event E
Total distance in which outcomes can lie
 =
(1/2)
 =

We now try to extend this idea for finding the probability as the ratio of the favourable area to the total area.