probability

                               PROBABILITY          

INTRODUCTION

—  Many events can't be predicted with total certainty. The best we can say is how likely they are to happen, using the idea of probability.

—  Probably Kuzhalisai will stand first in the forth coming annual examination. ™

—  Possibly Thamizhisai will catch the train today. ™

—  The prices of essential commodities are likely to be stable. ™

—   There is a chance that Leela will win today’s Tennis match.

—  The words “Probably”, “Possibly” , “Likely”, “Chance” , etc., will mean “the lack of certainty OR uncertainty”

EXAMPLES

—  “Should I carry an umbrella to work today?”, “Will my cellphone battery last until tonight?”, and “Should I buy a new brand of laptop?”. Probability provides a way to make decisions when the person is uncertain about the things, quantities or actions involved in the decision.

DEFINITION

—  Probability is the chance that something will happen - how likely it is that some event will happen.

—  Sometimes you can measure a probability with a number like "10% chance of rain", or you can use words such as impossible, unlikely, possible, even chance, likely and certain.
FORMULA:

—  Probability of an event happening = Number of ways it can happen / Total number of outcomes

EXAMPLES

Throwing Dice  :

•       When a single die is thrown, there are six possible outcomes: 1, 2, 3, 4, 5, 6.

•       The probability of any one of them is 1/6.

•       BASIC CONCEPTS:

•       Experiment

•       Trial

•       Sample space

•       Sample point

•       Events

EXPERIMENT:

v  An experiment is defined as a process whose result is

well defined.

v  There are two types of experiment.

1. Deterministic Experiment : It is an experiment whose outcomes can be predicted with certainty, under identical conditions.
2. Random Experiment : It is an experiment whose all possible outcomes are known, but it is not possible to predict the exact outcome in advance.                    

 Trial

A Trial is an action which results in one or several outcomes.

EXAMPLES:

“ Flipping” a coin and “Rolling” a die are trials                          

SAMPLE SPACE:

A sample space S is the set of all possible outcomes of a random experiment.

EXAMPLE:

•       While rolling a die, sample space

•        S = { 1, 2,3,4, 5, 6}                                                        

SAMPLE POINT:

Each outcome of an experiment is called a sample point.

EXAMPLE:

While rolling a die each outcome,

 {1} {2} {3} {4} {5} and {6}

 are are corresponding sample points .        

EVENTS:

—  Any subset of a sample space is called an event.

—  EXAMPLE:

—  When a die is rolled some of the possible events are {1, 2, 3}, {1, 3}, {2, 3, 5, 6}

APPLICATION:

many ways probability used in our life.

Examples:

1. every day you use probability to plan around the weather. Meteorologists can't predict exactly what the weather will be, so they use tools and instruments to determine the likelihood that it will rain, snow or hail. For example, if there's a 60-percent chance of rain, then the weather conditions are such that 60 out of 100 days with similar conditions, it has rained. You may decide to wear closed-toed shoes rather than sandals or take an umbrella to work. Meteorologists also examine historical data bases to guesstimate high and low temperatures and probable weather patterns for that day or week.
2. I’ve Got Your Number:
3. Produced in collaboration with Wales Institute of Mathematical and Computational Sciences, I’ve got your Number is a quiz show with a difference.                                                                                     Thank you.