CBSE Class 11 Mathematics Probability Notes

Class XI:

Math Chapter:

Probability Chapter Notes

Key Concepts

1. The theory of probability is a branch of mathematics that deals withuncertain or unpredictable events. Probability is a concept that gives a numerical measurement for the likelihood of occurrence of an event.

2. An act which gives some result is an experiment.

3. A possible result of an experiment is called its outcome.

4. The sample space S of an experiment is the set of all its outcomes.Thus, each outcome is also called a sample point of the experiment

5. An experiment repeated under essentially homogeneous and similarconditions may result in an outcome, which is either unique or not unique but one of the several possible outcomes.

6. An experiment is called random experiment if it satisfies the followingtwo conditions:

(i) It has more than one possible outcome.

(ii) It is not possible to predict the outcome in advance.

7. The experiment that results in a unique outcome is called adeterministic experiment.

8. Sample space is a set consisting of all the outcomes, its cardinality isgiven by n(S).

9. Any subset ‘E’ of a sample space for an experiment is called an event.

10.The empty set f and the sample space S describe events. In fact f iscalled an impossible event and S, i.e., the whole sample space is called the sure event.

11.Whenever an outcome satisfies the conditions, given in the event, wesay that the event has occurred.

12.If an event E has only one sample point of a sample space, it is calleda simple (or elementary) event. In the experiment of tossing a coin, the sample space is {H,T}and the event of getting a {H} or a {T}is a simple event. 

13.A subset of the sample space, which has more than on element is called a compound event. In throwing a dice, the event of appearing of odd numbers is a compound event, because E={1,3,5} has '3' sample points or elements in it.

14.Events are said to be equally likely, if we have no reason to believe that one is more likely to occur than the other. The outcomes of an unbiased coin are equally likely.

15.Probability of an event E, is the ratio of happening of the number of element in the event to the number of elements in the sample space.
(i) P(E) =n(E)/n(S) 
(ii) 0£P(E) £1

16.Independent Events: Two or more events are said to be independent if occurrence or non-occurrence of any of them does not affect the probability of occurrence or non-occurrence of the other event.

17.The complement of an event A, is the set of all outcomes which are not in A (or not favourable to) A. It is denoted by A’ .

18.Events Aand B are said to be mutually exclusive if and only if they have no elements in common. 

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