Quantitative Aptitude Free-Study Notes
20. PROBABILITY
A. Experiment :An operation which can produce some well-defined outcome is called an experiment
B.
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
Examples of performing random experiment:
(i)
rolling an unbiased dice
Details:
(i)
When we throw a coin. Then either a head(h) or a tail (t) appears.
C. Sample space :When we perform an experiment ,then the set S of all possible outcome is called the sample space. Denoted by ‘s’
Example of sample space:
(i)
in tossing a coin ,s = {h,t}
D.
Event:
Any subset of a sample space.
E.
Probability of occurrence of an event.
F.
Results on Probability:
(i)
P(S) = 1
(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
(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.
(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}.
let S be the sample space and E be the event . then,E⊆S.
P(E)=n(E)/n(S).
(ii)
0<P(E)<1
(iii)
P(φ)=0
(iv)
For any event a and b, we have: P(a∪b)=P(a)+P(b)-P(a∪b)
(v)
If A denotes (not-a),then P(A)=1-P(A).