we take a decision by guessing the future happening that is whether an event occurs or not.

Our decision comes true and sometimes it may not.

We try to measure numerically the chance of occurrence or non-occurrence of some events just as we measure many other things in our daily life.

This kind of measurement helps us to take decision in a more systematic manner.

Therefore we study probability to figure out the chance of something happening.

**Certain**: something that must occur Ex: Gandhiji’s birthday is on 2nd October.

**More likely** :something that would occur with great chance Ex: Vivek watching the cricket match

**Equally likely**** : **somethings that have the same chance of occurring Both teams winning the toss.

**Less likely** : Some thing that would occur with less chance Vivek doing homework on the day of cricket match.

**Impossible :**** **Something that cannot happen.

An activity which gives a result is called an **experiment.**

In such experiments though we know the possible outcomes before conducting the experiment we cannot predict the exact outcome that occurs at a particular time, in advance

**Random Experiment :** An experiment which can be repeated a number of times under the same set of conditions, and the outcomes are not predictable is called a Random Experiment.

**Trial :-** Performing an experiment is called a trial.

**Sample Space** :- The set of all possible outcomes is called the **sample space**

The **sample space ** of an experiment or random trial is the set of all possible outcomes or results of that experiment.

A sample space is usually denoted using **set notation**, and the possible outcomes are listed as elements in the set.

It is common to refer to a sample space by the labels ** S, Ω, or U** (for “universal set“).

Ex: if the experiment is tossing a coin, the sample space is typically the set {head, tail}.

For tossing two coins, the corresponding sample space would be {(H, H) , (H, T) , (T, H ) ,(T, T }.

For tossing a single six-sided die, the typical sample space is {1, 2, 3, 4, 5, 6}

**Probability:**

**Probability** is

the measure of

the likelihood that an event will

occur

the quantification into a numerical measure is

referred to as finding Probability

Probability can be found in two ways

i) Experimental Probability

ii) Theoretical probability

**Experimental Probability :**** **To find/estimate the probability in this method, the

experiment is done for more times and records the number of occurrences that

our favorable event occurred.

If A is an event then its experimental probability is

P(A) =

This probability is in deductive method.

**Experimental probability v/s theoretical probability**

Generally before the experiment, we estimate its theoretical probability. But after experiment we

can find that there is difference between experimental and theoretical

probability. If the experiment is done for more times, then the experimental

probability closes to the theoretical probability.

**Complementary events:-**

We denote the event ‘not E’ by . This is called the complement event of event E.

So, P(E) + P(not E) = 1

i.e., , which gives us

In general, it is true that for an event E,

the event E, representing not E, is called the compliment of the event E.

**impossible event**:- The probability of the event which is impossible to occur is 0. Such an event is called an **impossible event**.

**Sure ****or a ****certain event**:-** **The probability of an event which is sure (or certain) to occur is 1. Such an event is called a **sure **or a **certain event**.

**• **For an event E, we have 0 < P(E) < 1.

v **The probability of an event which is certain = 1**

v **The probability of an event which is impossible = 0**

v **The probability of an event always lies between 0 and 1 ( 0 and 1 inclusive)**

**Deck of cards**

**• **The pack or deck of playing cards consists of 52 cards**, **

**26 of red colou**r and **26 of black colour**.

There are four suits each of **13 cards namely**

red hearts (♥)-13 , king, queen, jack, 10, 9, 8, 7, 6, 5, 4, 3, 2, ace

diamonds (♦)- 13 king, queen, jack, 10, 9, 8, 7, 6, 5, 4, 3, 2, ace

black spades (♠)-13,and king, queen, jack, 10, 9, 8, 7, 6, 5, 4, 3, 2, ace

black clubs (♣)-13. king, queen, jack, 10, 9, 8, 7, 6, 5, 4, 3, 2, ace

Each suit contains ace, king, queen, jack or knave, 10, 9, 8, 7, 6, 5, 4, 3, 2, ace

There are 4 aces, 4 kings, 4 queens, 4 jacks, 4 tens, and so on in a pack.

Kings, queens, and jacks are called **face cards.**

** **

**Face cards 12 cards( J, K,Q) **

**number cards 36( 2 to 10)**