business mathematics

Probability concepts

Probability

Introduction:

Experiment:
An operation which can produce some well-defined outcome is
called an experiment.

Random Experiment:
An experiment in which all possible out comes are known and
the exact output cannot be predicted in advance is called a
random experiment.
EX:
1) Rolling an unbiased dice.
2) Tossing a fair coin.
3) Drawing a card from a pack of well-shuffled cards .
4)Picking up a ball of certain colour from a bag containing
balls of different colours.

Details:

1) When we thrown a coin ,then either a Head(H) or a Tail(T)
appears.
2)A dice is a solid cube ,having 6 faces,marked 1,2,3,4,5,6
respectively. When we throw a die ,the outcome is the number
that appears on its upper face.
3)A pack of cards has 52 cards.
It has 13 cards of each suit,namely spades,clubs,hearts and
diamonds. Cards of spades and clubs are balck cards.
Cards of hearts and diamonds are red cards.
There are four honours of each suit.
These are Aces,Kings,queens and Jacks.
These are called Face cards.

Sample Space:
When we perform an experiment ,then the set of S of all
possible outcomes is called the Sample space .

EX:
1)In tossing a coin S= {H,T}.
2)If two coins are tossed then S= {HH,HT,TH,TT}.
3)In rolling a dice ,we have S={1,2,3,4,5,6}.

Event:Any subset of a sample space is called an Event.
Probability of occurrence of an Event:
Let S be the sample space.
Let E be the Event.
Then E cS i.e E is subset of S then
probability of E p(E) =n(E)/n(S).

Reults on Probability:
1)P(S) =1.
2)0 < P(E) < 1
probability of an event lies between 0 and 1.
Max value of probability of an event is one.
3)P(Ф)=0.
4)For any events A and B we have .
P(AUB) =P(A) +P(B) -P(AnB).
5)If A denotes (not -A) then
P(A) =1-P(A)
P(A)+P(A) =1.