**INTRODUCTION **

**Often experiments are performed in order to produce observations or measurements that assist us in arriving at conclusions. These recorded informations in it’s original collected form are referred as ” raw data ” .**

**Mathematicians define experiment as any process or operation that generates raw data.**

**If a chemist runs an analysis several times under the same experimental conditions, he will not get concurrent result, which indicates an element of chance in the experimental procedure.**

**It is these chance outcomes that occur around us with which this chapter is basically concerned.**

__Random Experiment:__

__Random Experiment:__**An experiment, whose all possible outcomes are known in advance but the outcome of any specific performance can not be predicted before the completion of the experiment, is known as random experiment.**

**An example of random experiment might be tossing of a coin. This experiment consists of only two outcomes head or tail. Another example might be launching of a missile and observing the velocity at specified times. The opinions of voters concerning a new sales tax can also be considered as outcomes of random experiment.**

__Sample-space and sample point:__

__Sample-space and sample point:__**A set whose elements represent all possible outcomes of a random experiment is called the sample space and is usually represented by ‘ S ‘.**

**An element of a sample space is called a sample point.**

**Consider the experiment of tossing a die. If we are interested in the number that shows on the top face, then sample space would be S _{1} = {1, 2, 3, 4, 5, 6}**

**If we are interested only in whether the number is even or odd, then sample space is simply S**_{2}= {even, odd}**Clearly more than one sample space can be used to describe the outcomes of an experiment. In this case ‘ S _{1} ‘ provides more information than ‘ S_{2} ‘. If we know which element in S_{1} occurs, we can tell which outcome in S_{2} occurs; however, a knowledge of what happens in S_{2} in no way helps us to know which element in S_{1} occurs.**

**In general it is desirable to use a sample space that gives the maximum information concerning the outcomes of the experiment.**

**Suppose three items are selected at random from a manufacturing process. Each item is inspected and classified as defective or non-defective. The sample providing the maximum information would be S _{1} = {NNN, NDN, DNN, NND, DDN, DND, NDD, DDD}.**

**A second sample space, although it provides, less information, might be S _{2} = {0, 1, 2, 3} Where the elements represent no defectives, one defective, two defectives, or three defectives in our random selection of three items.**

**Event:**

**Event:**

**An event is a subset of sample – space.**

**In any sample space we may be interested in the occurrence of certain events rather than in the occurrence of a specific element in the sample space.**

**For instance, we might be interested in the event ‘ A ‘ that the outcome when die is tossed is divisible by 3.**

**This will occur if the outcome is an element of the subset**

**A = {3, 6}.**

**Clearly, to each event we can assign a collection of sample point(s), which constitute a subset of the sample space.**

**This subset represents all the elements for which the event is true.**

**For instance, given the subset A = {t | t < 5} of sample space S = {t | t ≥ 0}, where ‘ t ‘ is the life in years of a certain electronic component, ‘ A ‘ would represent the event that the component fails before the end of fifth year.**

__Simple Event & Compound Event :__

__Simple Event & Compound Event :__**If an event is a set containing only one element of the sample-space, then it is called a simple event.**

**A compound event is one that can be represented as a union of sample points.**

**For instance, the event of drawing a heart from a deck of cards is the subset A = {heart} of the sample space**

**S = {heart, spade, club, diamond}.**

**Therefore A is a simple event. However the event B of drawing a red card is a compound event since**

**B = {heart U diamond} = {heart, diamond}.**

**It must be noted that the union of simple events produces a compound event that is still a subset of sample space.**

**It should also be noted that if 52 cards of the deck were the elements of sample space rather than four suits, then event ‘ A ‘ would also be compound event.**