ThePrismSolutions

ThePrismSolutions

PROBABILITY

1.Experiment :

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

2.Random experiment:

An experiment in which all possible outcome are known and the exact out put cannot be predicted in advance is called an random experiment

Eg of performing random experiment:

(i)rolling an unbiased dice

(ii)tossing a fair coin

(iii)drawing a card from a pack of well shuffled card

(iv)picking up a ball of certain color from a bag containing ball of different colors

Details:

(i)when we throw a coin. Then either a head(h) or a tail (t) appears.

(ii)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 appear on its top face .

(iii)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 black cards Cards of hearts and diamonds are red cards There are 4 honors of each suit These are aces ,king ,queen and jack These are called face cards

3.Sample space :When we perform an experiment ,then the set S of all possible outcome is called the sample space. eg of sample space:

(i)in tossing a coin ,s={h,t}

(ii)if two coin are tossed ,then s={hh,tt,ht,th}.

(iii)in rolling a die we have,s={1,2,3,4,5,6}.

4.event:

Any subset of a sample space.

5.Probability of occurrence of an event.

let S be the sample space and E be the event . then,E⊆S.

P(E)=n(E)/n(S).

6.Results on Probability:

(i)P(S) = 1 (ii)0 <P(E)<1 (iii)P(∅)=0

(iv)For any event a and b, we have:

P(a⋂b)=P(a)+P(b)-P(a⋃b)


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