Class 10 Maths- Geometric Probablility

Geometric probability

The definition of the probability of occurrence of an event fails if the total number of outcomes (elementary events) of a trial in a random experiment is infinite. For example, if it is asked to find the probability that a point selected at random in a given region will lie in a specified part of that region, then the definition of Theoretical probability of an event: If there are ‘n’ elementary events associated with a random experiment and ‘m’ of them are favourable of an event A, then the probability of happening or occurrence of event A is denoted by byP(A) and is defined as the ratio .  In such cases, the definition of probability is modified and extended to what is called geometric probability. In such cases, the formula for finding the probability p of occurrence of an event is given by

p = 

Here, ‘measure’ means length, area or volume of the region or space.

Example: 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 the 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 as shown in figure.

Let A be the event that the music is stopped within the first half minute. Then, outcomes favourable to the event A are all points on the number line from O to Q i.e. from 0 to .

The total number of outcomes are the points on the numberline from O to P. i.e. from 0 to 2.

\P(A) 

Some real life examples include: