Probability Problems, Shortcut Tricks and Examples
Probability Examples  Page 2
Probability Questions  Page 3
Probability Lectures  Page 4
Probability In an experiment if ‘ n ‘ is the number of exhaustive cases and ‘m’ is the number of favourable cases of an event A. Then the probability of event A is denoted by P(A).
P(A) =
Probability Theory
 Random Experiment : An experiment in which all possible out comes are known and the exact output cannot be predicated in advance is called Random Experiment.
EXAMPLE :
(i) Tossing a fair coin
(ii) Rolling an unbiased dice
(iii) Drawing a card from a pack of well shuffled cards  Trail : Conducting a Random Experiment once is known as a Trail
 Outcome : The result of a Trail in the random experiment is called as Outcome
EXAMPLE : In tossing a single coin outcomes are H and T  Sample Space : A set of all possible outcomes of a random experiments is known as Sample Space
EXAMPLE :
( i ) In the experiment of tossing a coin the sample space S H,T
( ii ) If Two coins are tossed then S HH,HT,TH,TT
( iii ) In throwing a die S 1,2,3,4,5,6  Event : Any nonempty subset of a Sample Space is called an Event
EXAMPLE :
( i ). in Tossing a single coin getting Head or Tail is an Event
( ii )Getting an Ace (or) Diamond from a pack of 52 cards is an event  Exhaustive Events : The total number of possible outcomes of an experiment is known as Exhaustive Events
EXAMPLE : In the experiment of throwing a die the total number of possible outcomes = 6  Favourable Events : The number of event which favour the happing of the events are known as Favourable Cases (or) Events
EXAMPLE : In tossing two dice the number of cases favourable to getting the sum 3 is (2, 1), (1, 2) i.e., 2  Mutually Exclusive Events : If two events have no common outcomes then they are called Mutually Exclusive
EXAMPLE: In tossing a coin the events Head & Tail are mutually exclusive because Head & Tail cannot happen at the same time.  Independent Events : Two events are said to be independent if the happening of one event does not affect the happening of the other.
 Dependent Events : Two events are said to be dependent if the happening of an event will affect the happening of the other event .
EXAMPLE: If we draw a card from a pack of 52 cards and replace it before we draw a second card. The second card is independent of first one. If we don’t replace the first card before the second draw. The second draw depends on the first one.  Axioms of Probability : Let S be the sample space and A be the event i.e.,
1.
2. P(S) = 1
3. If A and B are mutually exclusive ( Disjoint i.e., )
= P(A)+P(B)  Results of Probability :
1. for any two events A & B ,
2. If denotes compliment of event A then , = 1P(A)
3. For any two events A & B ,
4. For any three events A, B & C ,
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