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# RD Sharma Class 12 Chapter 31 Solutions (Probability)

RD Sharma Class 12 Maths Solutions Chapter 31 Probability teaches you the concepts of probability. This chapter is one of the most important chapters in Class 12 Mathematics that is going to help you in advance studies as well. The topics you’ll learn in this chapter are Recapitulation of important terms and concepts, probability of an event, conditional probability, multiplication theorems on probability, more on conditional probability, independent events, More on theorems of probability, the law of total probability, Baye’s theorem, etc.

RD Sharma Class 12 Maths Solutions Chapter 31 Probability discusses 151 Questions in 7 exercises. These questions give you a rough idea about the pattern of CBSE and entrance exam questionnaire you can expect. All these questions have covered every single topic that you’ve learnt in Probability.

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## Some topics discussed in RD Sharma Class 12 Maths Solutions Chapter 31 Probability

• Random Experiment – Consider an experiment. If you repeat it under identical conditions, it will not produce the same outcome every time. However, the outcome in every trial is one of the many outcomes. Such an experiment is known as a random experiment. You may also call it a probabilistic experiment.
• Elementary Event – Performing a random experiment will generate outcomes. These outcomes are elementary events.
• Sample Space – When a random experiment is performed, then the set of all of its possible outcomes are known as the sample space that is associated with the experiment.
• Event – As the random experiment is performed, there is a subset of the sample space that is associated with this experiment. This subset is called an event.
• The occurrence of an Event –  While performing a random experiment, an event that associates with it will occur if and only if any elementary event belonging to that becomes the outcome.
• Certain (or sure) Event – A random experiment is performed. An event that associates with that experiment will be a certain event if it occurs every time when you perform an experiment.
• Impossible Event – A random experiment is performed. An event associated with this experiment will be known as an impossible event if it never occurs anytime you perform an experiment.
• Compound Event – On performing a random experiment, an event associated with it is known as a compound event, if it is found to be a disjoint union of two or more than two elementary events.
• Mutually Exclusive Events – A random experiment is performed. Then two events or more than two events will be known as mutually exclusive or impossible if the occurrence of any of the two will prevent the occurrence of the rest, i.e. if no two or more than two events occur simultaneously during the same trial.
• Exhaustive events – A random experiment is performed. And two events or more than two events that are associated with the random experiment are known as exhaustive if their union is found to be a sample space.

### Discussion of exercises in RD Sharma Class12 Maths Solutions Chapter 31 Probability

1. Exercise 31.1 covers questions on conditional probability and are also based upon its meaning. The exercise has 9 questions.
2. Exercise 31.2 tests your understanding of multiplication theorems on probability, finding the probability of simultaneous occurrence of two or more events, etc. This exercise has 13 questions in total.
3. Exercise 31.3 will discuss the concepts of properties of conditional probability. This exercise covers 26 questions.
4. Exercise 31.4 is about independent events such as pairwise independent, mutually independent, etc. It also asks questions on independent experiments. The exercise will cover questions such as proving the independence or dependence of given events, etc.
5. Exercise 31.5 covers questions on theorems of probability.
6. Exercise 31.6 has a complete questionnaire on the law of total probability, etc. This exercise has 12 questions in total.
7. Exercise 31.7 is the last exercise of Probability in RD Sharma Solutions and discusses questions on Baye’s Theorem, etc. The exercise contains a total of 33 questions.

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