# Probability Class 10 Notes: Chapter 15

## CBSE Class 10 Maths Probability Notes:-

The branch of mathematics that measures the uncertainty of the occurrence of an event using numbers is called probability. The chance that an event will or will not occur is expressed on a scale ranging from 0-1.
It can also be represented as a percentage, where 0% denotes an impossible event and 100 % implies a certain event.

### Event and outcome

An Outcome is a result of a random experiment. For example, when we roll a dice getting six is an outcome.
An Event is a set of outcomes. For example when we roll dice the probability of getting a number less than five is an event.
Note: An Event can have a single outcome.

## Experimental Probability

Experimental probability can be applied to any event associated with an experiment that is repeated a large number of times.
A trial is when the experiment is performed once. It is also known as empirical probability.
Experimental or empirical probability: P(E) =Number of trials  where the event occurred/Total Number of Trials

## Theoretical Probability

Theoretical Probability, P(E) = Number of Outcomes Favourable to E / Number of all possible outcomes of the experiment

Here we assume that the outcomes of the experiment are equally likely.

### Elementary Event

An event having only one outcome of the experiment is called an elementary event.
Example: Take the experiment of tossing a coin n number of times. One trial of this experiment has two possible outcomes: Heads(H) or Tails(T). So for an individual toss, it has only one outcome, i.e Heads or Tails.

### Sum of Probabilities

The sum of the probabilities of all the elementary events of an experiment is one.
Example: take the coin-tossing experiment. P(Heads) + P(Tails )

(1/2)+ (1/2) =1

### Impossible event

An event that has no chance of occurring is called an Impossible event, i.e. P(E) = 0.
E.g: Probability of getting a 7 on a roll of a die is 0. As 7 can never be an outcome of this trial.

### Sure event

An event that has a 100% probability of occurrence is called a sure event. The probability of occurrence of a sure event is one.
E.g: What is the probability that a number obtained after throwing a die is less than 7?
So,  P(E) = P(Getting a number less than 7) = 6/6= 1

### Range of Probability of an event

The range of probability of an event lies between 0 and 1 inclusive of 0 and 1, i.e. 0P(E)1.

## Geometric Probability

Geometric probability is the calculation of the likelihood that one will hit a particular area of a figure. It is calculated by dividing the desired area by the total area. In the case of Geometrical probability, there are infinite outcomes.

## Complementary Events

Complementary events are two outcomes of an event that are the only two possible outcomes. This is like flipping a coin and getting heads or tails. $P(E)+P(\bar{E}) = 1$, where E and $\bar{E}$ are complementary events. The event $\bar{E}$, representing ‘not E‘, is called the complement of the event E.