# Probability Class 10 Notes Maths Chapter 15

### CHAPTER AT A GLANCE

1. Probability-An Experimental (Empirical) Approach

Let n be the total number of trials. The empirical probability of an event E happening is given by

2. Rational Numbers and Their

(I) Experiment : An operation which can produce some well-defined outcomes is known as experiment
(ii) Trial : Performing of an experiment is called trial.
(iii) Equally likely outcomes : Outcomes of trial are equally likely if there is no reason to accept one in preference to the others.
(iv) Sample space : The set of all possible outcomes of an experiment is called sample space.
(v) Elementary event : An event having only one outcome

Note : that the sum of probabilities of all the elementary events of an experiment is 1.

3. Probability-A Theoretical Approach (Classical Probability)

If an event ‘A’ can happen in ‘m’ ways and does not happen in ‘n’ ways, then the probability of occurence of event ‘A’ denoted by P (A) is given by Number of favourable outcomes m

4. Probability of lmpossible and Sure Events

The probability of an event which is impossible to occur is O and such an event is called impossible event.
i.e; for impossible event ‘I’,P(I) = 0
The probability of an event which is sure or certain to occur is 1 and such an event is called sure event or certain event.
i.e; for sure event or certain event,’s’, P(s)=1
5. Range of the Probability of an Event

From the definition of the probability P(E),we see that the numerator (number of outcomes favorable to the event E) is always equal or greater than O but less than or equal to the denominator (the number of all possible outcomes). Therefore,

6. Complementary Events

The event representing (‘notE) is called the complement of event ‘E’ and we say that the events E and E are complementary events,

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