♣ Random experiment
☺An experiment in which results
are unpredictable
♣ Outcome
☺Results of a random experiment
♣ Exhaustive outcome
☺All possible occurrence of
outcomes in a random experiment
♣ Mutually exclusive event
☺Occurrence of one event
precludes or prevents the
occurrence of other event in a
random experiment.
♣ Equally likely event
☺Every outcome of a random
experiment which occur will have
an equal chance
♣ Independent event
☺Every outcome of a random
experiment will occur
independently of each other

♣ Favourable outcome
☺An event in which one is
interested in a random experiment
Sample space
The set of all possible outcomes of a random experiment is called sample space denoted by .

Example:
 = {NNN, NND, NDN, DNN, NDD, DND, DDN, DDD}
Event
A subset of the sample space  is known as an event. That is an event is a set consisting of possible outcomes of the random experiment. If the outcome of the experiment is contained in A, then we say that A has occurred.
Example: A = {x: x one defective chip is
found}
Algebra of events
Union: Suppose A and B are any two events then A  B = {x: x  A or x  B}

Example: If
A = {a card drawn at random from a
deck of cards is a jack}
B = {a card drawn at random from a
deck of cards is a diamond}
then A  B = {x: x is either a card
drawn randomly is a jack
or a diamond}.

Example 2: An unbiased die is thrown.
Let A = {an event that the outcome is
an odd number}
B = {an event that the outcome is
number  3}
then A  B = {x: x=1, 3, 4, 5, 6}.

Intersection: Suppose A and B are any two events then
A  B = {x: x  A and x  B}
Example 1: If
A = {a card drawn at random from a deck of
cards is a jack}
B = {a card drawn at random from a deck of
cards is a diamond}
then A  B = {x: x is a card drawn at
random from a deck of
cards is a jack}.

Example 2: An unbiased die is thrown.
Let A = {an event that an outcome is
an odd number}
B = {an event that an outcome is  3}
A  B = {x: x= 3, 5}.
Complement of events: Suppose  is a sample space and A be any event then
Ac = {x: x   but x  A}
Example 1: An unbiased die is thrown.
Let ={x: 1x6 }
A={an event that an outcome is  3}
Ac = {x: 1x2 }.

Posted in Posted by waytofeed at 8:46 AM