Probability is the measure of uncertainty of various
phenomenon, numerically. It can have positive Types of Event
value from 0 to 1. i. Impossible and Sure Events
ii. Simple Event
The words ‘probably’, ‘doubt’, ‘most probably’,
iii. Compound Event
‘chances’, etc., used in the statements above
involve an element of uncertainty.
Impossible and Sure Events:
𝑛𝑜. 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒
𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 = The empty set 𝜙 and the sample space S
𝑡𝑜𝑡𝑎𝑙 𝑛𝑜. 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 describe events. Impossible event is denoted
by φ, while the whole sample space, S, is called
Approach to Probability:
the Sure Event.
i. Statistical approach : Observation & data
E.g. in rolling a die, impossible event is that
collection
number is more than 6 & Sure event is the
ii. Classical approach: Only Equal probable
event of getting number less than or equal to 6.
events
iii. Axiomatic approach: For real life events. It
Simple Event:
closely relates to set theory.
If an event E has only one sample point of a
2. Random Experiments: sample space, it is called a simple (or
An experiment is called random experiment if it elementary) event.
satisfies the following two conditions: In a sample space containing n distinct
elements, there are exactly n simple events.
(i) It has more than one possible outcome. E.g. in rolling a die, Simple event could be the
(ii) It is not possible to predict the event of getting 4.
outcome in advance.
Compound Event:
Outcomes: a possible result of a random
If an event has more than one sample point, it
experiment is called its outcome.
is called a Compound event.
Sample space: Set of all possible outcomes of a E.g. in rolling a die, Simple event could be the
random experiment is called sample space. It is event of getting even number
denoted by the symbol S. Example: In Toss of a
coin, Sample space is Head, Tail. Algebra of Events
i. Complementary Event
Sample point: Each element of the sample space ii. Event ‘A or B’
is called a sample point. E.g. in toss of a coin, iii. Event ‘A and B’
Head is a Sample point. iv. Event ‘A but not B
3. Event:
It is the set of favorable outcome.
Any subset E of a sample space S is called an event. Complementary Event
E.g. Event of getting odd outcome in a throw of a Complementary event to A= ‘not A’
die Example: If event A= Event of getting odd
Occurrence of an event: the event E of a sample number in throw of a die, that is {1, 3, 5}
space S is said to have occurred if the outcome 𝜔 Then, Complementary event to A = Event of
of the experiment is such that 𝜔 ∈ 𝐸. If the getting even number in throw of a die, that is
outcome 𝜔 is such that 𝜔 ∉ E, we say that the {2, 4, 6}
event E has not occurred.
phenomenon, numerically. It can have positive Types of Event
value from 0 to 1. i. Impossible and Sure Events
ii. Simple Event
The words ‘probably’, ‘doubt’, ‘most probably’,
iii. Compound Event
‘chances’, etc., used in the statements above
involve an element of uncertainty.
Impossible and Sure Events:
𝑛𝑜. 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒
𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 = The empty set 𝜙 and the sample space S
𝑡𝑜𝑡𝑎𝑙 𝑛𝑜. 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 describe events. Impossible event is denoted
by φ, while the whole sample space, S, is called
Approach to Probability:
the Sure Event.
i. Statistical approach : Observation & data
E.g. in rolling a die, impossible event is that
collection
number is more than 6 & Sure event is the
ii. Classical approach: Only Equal probable
event of getting number less than or equal to 6.
events
iii. Axiomatic approach: For real life events. It
Simple Event:
closely relates to set theory.
If an event E has only one sample point of a
2. Random Experiments: sample space, it is called a simple (or
An experiment is called random experiment if it elementary) event.
satisfies the following two conditions: In a sample space containing n distinct
elements, there are exactly n simple events.
(i) It has more than one possible outcome. E.g. in rolling a die, Simple event could be the
(ii) It is not possible to predict the event of getting 4.
outcome in advance.
Compound Event:
Outcomes: a possible result of a random
If an event has more than one sample point, it
experiment is called its outcome.
is called a Compound event.
Sample space: Set of all possible outcomes of a E.g. in rolling a die, Simple event could be the
random experiment is called sample space. It is event of getting even number
denoted by the symbol S. Example: In Toss of a
coin, Sample space is Head, Tail. Algebra of Events
i. Complementary Event
Sample point: Each element of the sample space ii. Event ‘A or B’
is called a sample point. E.g. in toss of a coin, iii. Event ‘A and B’
Head is a Sample point. iv. Event ‘A but not B
3. Event:
It is the set of favorable outcome.
Any subset E of a sample space S is called an event. Complementary Event
E.g. Event of getting odd outcome in a throw of a Complementary event to A= ‘not A’
die Example: If event A= Event of getting odd
Occurrence of an event: the event E of a sample number in throw of a die, that is {1, 3, 5}
space S is said to have occurred if the outcome 𝜔 Then, Complementary event to A = Event of
of the experiment is such that 𝜔 ∈ 𝐸. If the getting even number in throw of a die, that is
outcome 𝜔 is such that 𝜔 ∉ E, we say that the {2, 4, 6}
event E has not occurred.
