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Chapter 13 Class 12 Probability

Get NCERT solutions of all examples, exercises and Miscellaneous questions of Chapter 13 Class 12 Probability with detailed explanation. Formula sheet also available.


We started learning about Probability from Class 6,

we learned that Probability is Number of outcomes by Total Number of Outcomes.

In Class 11, we learned about Sample Space, Events, using Sets


In this chapter, we will learn about

  • Conditional Probability - Finding probability of something when an event has already occurred. For example - finding probability of 4 coming in second throw of die if 6 has come in first throw. We also discuss its formula, properties and questions
  • Independent events - What is an independent event, and where is it used?
  • Multiplication rule of probability - We learn about dependent and independent events, and the multiplication rule for 2, or more than two events
  • Basic Probability - We solve questions using basic formula - Number of outcomes/Total Outcomes to find Probability, set theory, and permutation and combinations to find probability.
  • Theorem of total probability - We use the formula P(A) = P(B) P(A|B) + P(B') P(A|B')
  • Bayes theorem - Finding probability when an event has already happened
  • Random Variable - Writing random variable 
  • Probability distribution - Finding probability distribution of random variable, and finding its mean (or expectation)
  • Variance and Standard Deviation of a Random Variable - Finding variance and standard deviation using probability distribution
  • Bernoulli Trials - Checking if an event is a Bernoulli trial
  • Binomial Distribution - For Bernoulli Trial, finding probability using Binomial Distribution


Check the chapter from different Concepts, starting from Basic to Advanced, or you can also refer to the exercises mentioned in the NCERT Book. Click on a topic below to start