2. What is Probability?
Probability is simply how likely something is to happen.
Or
The numerical value representing the chance, likelihood, or possibility that a certain
event will occur (always between 0 and 1).
3. Example
Coin Tossing :
• When a coin is tossed , there are two possible outcomes assuming
all outcomes are equally likely : Head and Tail .
• So the probability of occurrence of head when a coin is tossed once
is P(H): 0.5
• The probability of occurrence of tail when a coin is tossed once is
P(T): 0.5
4. Event :
Each possible outcome of a variable is an event.
Example of an event : Rolling a die
Example of Sample space : 6
Sample Space :
is the collection of all possible events
5. Event types
Mutually exclusive Events
Events that cannot occur
simultaneously.
Collectively exhaustive events
One of the events must occur.
The set of events cover the entire
sample space.
6. Properties of Probability
The probability of any event A is a number between 0 and 1, i.e., 0 ≤ P(A) ≤ 1.
0 indicates an impossible event such as rolling 7 on a six-sided die and 1 indicates
that the event will certainly happen such as the sun rises in the east.
The sum of the probabilities of any set of mutually exclusive and exhaustive
events equals 1. P(A)+P(B)+P(C)=1 If A,B,C are mutually exclusive and collectively
exhaustive.
7. Addition Rule
• For any two events A and B , P(A or B) = P(A) + P(B) –P(A and B)
• If A and B are mutually exclusive , then P(A and B)=0, P(A or B) = P(A) +
P(B)
8. Conditional Probability
• A conditional probability is the probability of one event, given that another event has
occurred.
P(B|A) = P(A and B) / P(A)
OR
P(B|A) = P(A∩B) / P(A) ,where P = Probability, A = Event A, B = Event B
9. Bayes Theorem
• Bayes’ Theorem is used to revise previously calculated probabilities based
on new Information.
• It is an extension of conditional probability.
