P( A I B) is the probability of occurrence of event A given that event B has already occurred, P(B) is not equal to zero. The formula is:

P( A I B ) = (number of outcomes favourable to A∩B) / (number of outcomes favourable to B). 

Hence, P( A I B ) = P(A∩B) / P( B ) and P ( B I A ) = P(A∩B) / P( A ).

They are used to track outcomes of a sequence of events. Here, from each end of these lines a line is drawn for each possible outcome from the next event and so on until the final outcome of all events is reached. 

For example, the following image explains the probability tree of the event of tossing a coin twice.

NCERT Solutions Class 12 Probability states that there are three major types of probabilities:

• Theoretical Probability
• Experimental Probability
• Axiomatic Probability

Theoretical probability

• It is based on the possible chances of an event occurring. 
• It can be calculated based on the reasoning behind the probability of an event.
• For example, if a coin is tossed, the theoretical probability of getting a head is ½.

Experimental Probability

• It is based on the basis of the observations of an experiment. 
• It can be calculated by dividing the number of possible outcomes by the total number of trials. (Number of possible outcomes / Total number of slides)
• For example, if a coin is tossed 15 times and head is recorded 6 times then the experimental probability for heads is 6/15, which is equal to 2/5.

Axiomatic Probability

• According to NCERT Solutions Class 12 Probability, there are a set of axioms also known as Kolmogorov’s three axioms. They are as follows:
• Axiom 1: Probability of event 
• Axiom 2: Probability of sample space 
• Axiom 3: Mutually exclusive events
• Conditional Probability: It is the likelihood of an event or outcome occurring based on the occurrence of a previous event or outcome.

Probability of an Event

An event A can occur in ‘n’ ways out of a sum of ‘m’ probable or possible equally likely ways.

Thus, P(A) = n/m

The probability that the event will not occur or be known as its failure is expressed as:

P(A’) = (m-n)/n = 1-(n/m)

Thus, P(A) + P(A’) = 1

Therefore, the sum total of all probable events in a random test is one.

These are events that have the same theoretical probability of happening. For example,

• Getting 1 and 4 on throwing a die
• Getting a head or tail while tossing a coin

It is the possibility that there will be only two outcomes that state that an event will either occur or not. For example, 

• The possibility of raining or not raining.
• Getting a head or tail while tossing a coin.

• The probability function PDF represents the density of a continuous random variable falling between a given range of values.
• The probability density function is used to describe normal distribution, as well as mean and deviation.

Chapter 13 for class 12 Maths Probability is an essential subject as well as a difficult one with many problems, diagrams and concepts. 

Key points of this chapter are:

• Easy language and eye-catching formats.
• Topics as per the latest syllabus pattern so students can revise the notes in minimum time with maximum accuracy.
• Follows the guidelines of the CBSE syllabus.
• After studying Determinants Class 12 NCERT Solutions notes, students will be more confident when presented with other enormous textbooks.
• Covers all necessary formulas and concepts presented in the chapter.
• On studying these notes, students won’t have to spend much time revising before the exams.

1. How many topics and sub-topics are there in this chapter?

There are 8 topics in Probability Class 12 NCERT with several subtopics under types of probability. 

2. Why is MSVgo NCERT Solutions for Class 12 Maths Chapter 13 reliable?

MSVgo notes are informative and on point. They are high yielding and help students in solving several objective and challenging questions. They concentrate both on the basics and the advanced aspects of the topic while maintaining integrity and effectiveness.

3. How to prepare for Probability Class 12?

Practice all the questions given in Probability NCERT Solutions Class 12 both solved and miscellaneous. In addition, make the most of the video lectures and notes available.

4. What videos should we refer for CBSE Class 12 Maths?

The videos related to class 12 NCERT Maths can be accessed from this website whenever necessary. They are valuable learning assets that can solve any query. In a nutshell, they can improve performance and become part of an interactive learning session. They speed up a student’s problem-solving skills and clarify doubts by simplifying difficult concepts.

5. How do I get notes for CBSE Class 12 Maths Chapter 13 Probability?

Notes for Probability NCERT Solutions Class 12 need to penned down by hand or viewed from reliable sources such as MSVgo notes.