BASIC CONCEPTS OF PROBABILITY

• PROBABILITY
  BUSINESS STATISTICS
  RESEARCH METHODOLOGY
  
  
• INTRODUCTION

1. IN DAY TO DAY LIFE,WE ALL MAKE USE OF THE WORD PROBABILITY.LIKE PROBABILITY IT MAY RAIN OR IT IS LIKELY THAT HE MAY NOT TURN UP TODAY. IT MEANS THE EVENTS ARE NOT CERTAIN TO TAKE PLACE.
2. THERE IS INVOLVED AN ELEMENT OF UNCERTAINTY OR CHANCE . THE AIM OF PROBABILITY THEORY IS T PROVIDE A MEASURE OF UNCERTAINTY.
3. THE THEORY OF PROBABILITY OWES ITS ORIGIN TO THE STUDY OF GAMES OF CHANCE LIKE GAMES OF CARDS,TOSSING COINS,DICE ETC

• BASIC CONCEPTS
• AN EXPERIMENT:- WHEN WE CONDUCT A TRIAL TO OBTAIN SOME STATISTICAL INFORMATION IT IS CALLED AN EXPERIMENT.

1. TOSSING OF A FAIR COIN IS AN EXPERIMENT AND IT HAS TWO POSSIBLE OUTCOMES. HEAD (H) OR TAIL(T)
2. ROLLING A FAIR DIE IS AN EXPERIMENT AND IT HAS SIX POSSIBLE OUTCOME,APPEARANCE OF  OR 2 OR 3 OR 4 OR 4 OR 5 OR 6
3. DRAWING A CARD FROM A WELL SHUFFLED PACK OF PLAYING CARDS IS AN EXPERIMENT AND IT HAS 52 POSSIBLE OUTCOMES

• EVENTS: THE POSSIBLE OUTCOMES OF TRIAL/EXPERIMENT ARE CALLED EVENTS. EVENTS ARE GENERALLY DENOTED BY CAPITAL LETTERS A,B AND C

1. IF FAIR COIN IS TOSSD THE OUTCOME LEADS TO HEAD OR TAIL ARE CALLED EVENTS
2. IF FAIR DIE IS ROLLED,THE OUTCOME MAY BE 1 OR 2 OR 3 OR 4 OR 5 OR 6

• EXHAUSTIVE EVENTS

1. IF ALL THE POSSIBLE OUTCOMES OF A TRIAL/EXPERIMENTS ARE TAKEN INTO CONSIDERATIONS THEN SUCH EVENTS ARE CALLED EXHAUSTIVE EVENTS.
2. IN CASE OF TOSSING A DIE,THE SET OF SIX POSSIBLE OUTCOME
3. IN CASE OF TOSSING A COIN THE SET OF TWO OUTCOMES H AND T ARE EXHAUSTIVE EVENTS.
4. IN CASE OF TWO DICE THE SET OF POSSIBLE OUTCOMES ARE 6X6=36

1.       EQUALLY LIKELY EVENTS

2.       IF EVENTS ARE SAID TO BE EQUALLY –LIKELY IF THE CHANCE OF HAPPENING OF EACH EVENT IS EQUAL OR SAME.

3.       IF A FAIR COIN IS TOSSED ,THE EVENTS H AND T ARE EQUALLY –LIKELY EVENTS

4.       IF A DIE IS ROLLED ANY FACE IS LIKELY TO COME UP AS ANY OTHER FACE.

• MUTUALLY EXCLUSIVE EVENTS

1. TWO EVENTS ARE SAID TO BE MUTUALLY EXCLUSIVE WHEN THEY CAN NOT HAPPEN SIMULTANEOUSLY IN SINGLE TRIAL.
2. TWO EVENTS ARE SAID TO BE MUTUALLY EXCLUSIVE WHEN THE HAPPENING OF ONE EXCLUDED THE HAPPENING OF OTHER IN SINGLE TRIAL.
3. IF WE THROW A COIN ,IF HEAD APPEARS THEN TAIL IS NOT POSSIBLE

• COMPLEMENTARY EVENTS

1. LET THERE BE TWO EVENTS A AND B. A IS CALLED THE COMPLEMENTARY EVENT OF B AND B IS CALLED COMPLEMENTARY EVENT IF A AND B ARE MUTUALLY EXCLUSIVE AND EXHAUSTIVE.
2. IN TOSSING A COIN,OCCURRENCE OF HEAD (H) AND TAIL (T) ARE COMPLIMENTARY EVENTS
3. IN TOSSING A DIE OCCURRENCE OF AN EVEN NUMBER (2,4,6) AND ODD NUMBER (1.3.5) ARE COMPLEMENTARY EVENTS

• SIMPLE AND COMPOUND EVENTS:

1. IN SIMPLE EVENTS WE CONSIDER THE PROBABILITY OF HAPPENING OR NOT HAPPENING OF SINGLE EVENTS
2. IN CASE OF COMPOUND EVENTS WE CONSIDER THE OCCURRENCE OF JOINT OCCURRENCE OF TWO OR MORE EVENTS.
3. IF TWO COINS ARE TOSSED SIMULTANEOUSLY WE SHALL FIND THE PROBABILITY OF GETTING TWO HEADS THEN WE ARE DEALING WITH COMPOUND EVENTS

• INDEPENDENT EVENTS:- TWO EVENTS ARE SAID TO BE INDEPENDENT IF THE OCCURRENCE OF ONE DOES NOT AFFECT AND IS NOT AFFECTED BY THE OCCURRENCE OF THE OTHER
• IN TOSSING A COIN TWICE,THE EVENT OF GETTING A HEAD IN THE SECOND THROW IS INDEPENDENT OF GETTING HEAD IN I ST THROW
• DEPENDENT EVENTS:-TWO EVENTS ARE SAID TO DEPENDENT WHEN THE OCCURRENCE OF ONE DOES NOT AFFECT THE PROBABILITY OF THE OCCURRENCE OF THE OTHER.
• THE PROBABILITY OF DRAWING A KING IS 4/52-1/13 BUT WHEN IT IS NOT REPLACED THE PROBABILITY OF KING IS 3/51