Definition of Probability
Probability is a branch of mathematics that deals with the occurrence of a random event. The value is expressed between zero and one. It helps to predict how likely events are to happen.
For example, when we toss a coin, either we get Head OR Tail, only two possible outcomes are possible (H, T).
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using probability. Probability can range in between 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. Probability for class 10 is an important topic for the students which explains all the basic concepts of this topic.
Note: The probability of all the events in a sample space sums up to 1. 
Contents in Probability:
 Definition
 Video Lectures
 Line of Probability
 Formula
 Types
 Probability Tree
 Probability Terms
 Probability Examples
Download this lesson as PDF: Probability PDF 
Probability Video Lectures
Probability Formula
Probability of event to happen P(E) = Number of favourable outcomes/Total Number of outcomes 
Learn More: All Probability Formulas
Probability Tree
Probability tree diagram helps to organize and visualize the different possible outcomes. Branches and ends of the tree are two main positions. Probability of each branch is written on the branch, whereas the ends are containing the final outcome. Tree diagram used to figure out when to multiply and when to add. You can see below a tree diagram for the coin:
Types of Probability
There are three major types of probabilities:
 Theoretical Probability
 Experimental Probability
 Axiomatic Probability
Theoretical Probability
It is based on the possible chances of something to happen. The theoretical probability is mainly based on the reasoning behind probability. For example, if a coin is tossed, the theoretical probability of getting a head will be Â½.
Experimental Probability
It is based on the basis of the observations of an experiment. The experimental probability can be calculated based on the number of possible outcomes by the total number of trials. For example, if a coin is tossed 10 times and heads is recorded 6 times then, the experimental probability for heads is 6/10 or, 3/5.
Axiomatic Probability
In axiomatic probability, a set of rules or axioms are set which applies to all probability types. These axioms are set by Kolmogorov and are known as Kolmogorov’s three axioms. With the axiomatic approach to probability, the chances of occurrence or nonoccurrence of the events can be quantified. The axiomatic probability lesson covers this concept in detail with Kolmogorov’s three rules (axioms) along with various examples.
One other type of probability that is Conditional Probability is the likelihood of an event or outcome occurring based on the occurrence of a previous event or outcome. This is explained in detail in probability for class 12.
Probability Term
Some of the important probability terms are discussed here:
Term  Definition  Example 

Sample Space  The set of all the possible outcomes to occur in any trial 

Sample Point  It is one of the possible results  In a deck of Cards:

Experiment or Trial  A series of actions where the outcomes are always uncertain.  The tossing of a coin, Selecting a card from a deck of cards, throwing a dice. 
Event  It is a single outcome of an experiment.  Getting a Heads while tossing a coin is an event. 
Outcome  Possible result of a trial/experiment  T (tail) is a possible outcome when a coin is tossed. 
Complimentary event  The nonhappening events. The complement of an event A is the event not A (or Aâ€™)  Standard 52card deck, A = Draw a heart, then Aâ€™ = Donâ€™t draw a heart 
Impossible Event  The event cannot happen  In tossing a coin, impossible to get both head and tail 
Probability Examples
Question 1: Find the probability of rolling a â€˜3 with a die.â€™
Solution:
Sample Space = {1, 2, 3, 4, 5, 6}
Number of favourable event = 1
Total number of outcomes = 6
Thus, Probability = 1/6
Example 2: Draw a random card from a pack of cards. What is the probability that the card drawn is a face card?
Solution:
A standard deck has 52 cards.
Total number of outcomes = 52
Number of favourable events = 4 x 3 = 12 (considered Jack, Queen and King only)
Probability = Number of Favourable Outcome/Total Number of Outcomes = 12/52= 3/13.
Probability Density FunctionÂ
The Probability Density Function(PDF) is the probability function which is represented for the density of a continuous random variable lying between a certain range of values. Probability Density Function explains the normal distribution and how mean and deviation exists. TheÂ standard normal distributionÂ is used to create a database or statistics, which are often used in science to represent the realvalued variables, whose distribution are not known.