NCERT Example 10 — Probability

NCERT Example

Example 10

geometrical probability · number line · time interval

In a musical-chair game, the music may stop at any time within 2 minutes after it begins. Find the probability that it stops within the first half-minute.

NCERT marks this example as not from the examination point of view.

Number line from 0 to 2 with one-half marked between 0 and 1. — Figure 14-1 from the supplied NCERT chapter.

Solution

Board-exam working:

All stopping times from 0 to 2 minutes are equally likely along the interval.

\text{Total interval length}=2\text{ minutes}

\text{Favourable interval length}=\frac12\text{ minute}

P(E)=\frac{\text{favourable length}}{\text{total length}}

P(E)=\frac{\frac12}{2}=\frac14

Final answer

\boxed{P(E)=\frac14}