### 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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