This document discusses different types of probability and theorems related to probability calculations. It defines probability, theoretical probability, experimental probability, and subjective probability. It then explains the theorem of total probability, which calculates the total probability of an event by considering mutually exclusive events related to that event. Next, it introduces Bayes' theorem, which provides a mathematical rule for revising estimates based on new information or observations. Finally, it defines the theorem of compound probability, which is the probability of two events occurring simultaneously, and provides formulas for calculating compound probability for independent and dependent events.

1. THEOREM OF TOTAL AND
COMPOUND PROBABILITY

2. What Is Probability ?
⮚ In simple terms, Probability is an
expectations.
⮚ It always lies within 0 to 1.00% to
100%)
⮚ In our regular life, we face lot of problem, in which we supposed to use
term like may be .., hope fully .. Etc.
⮚ By definition it is the ratio of favorable number of cases over total
number of cases.
⮚ The concept of probability is necessary in work with physical biological
or social mechanism that generate observation that can not be
predicted with certainty.

3. Probability Of An Event:

4. Types of Probability:
Theoretical Probability
❖ Probability which comes
from thought experiment
is called theoretical
probability.
• It is also called
classical probability.
It is calculated as follows:
Experimental Probability
❖ Probability which comes
from practical experiment
is called experimental
probability.
• It is also called empirical
probability.
• It is found by repeating an
experiment and observing
the outcome.
It is calculated as
Subjective Probability
❖ Probability which comes
from an educated guess
is called subjective
probability.
• It is found by observing
and analyzing the past
data.
• When the probability of
something happening
differs from person to
person, it is likely a
subjective probability.

5. Theorem Of Total Probability:
Total probability or the law of total probability is a theorem which helps
to calculate the total probability of an event. We calculate the total
probability by taking into account several other distinct events that are
disjoint from each other but are related to the event under
consideration.

6. Bayes' theorem:
⮚ The Bayes Theorem was developed and named for
Thomas Bayes(1702-1761).
⮚ Show the Relation between one conditional probability and its
inverse.
⮚ Provide a mathematical rule for revising an estimate or forecast in
light of experience and observation.

7. Theorem Of Compound Probability:
Compound probability which is also the joint probability is the
probability of two events of an experiment occurring simultaneously. We
can calculate the compound probability can be calculated for both
independent as well as the dependent variable.
▪ For dependent variables, we use the concept of conditional
probability specifically Bayes’ theorem.
▪ There are different formulas for calculating the two types of
compound events:
Say A and B are two events, then for mutually exclusive events: P(A
or B) = P (A) + P(B).
For mutually inclusive events, P (A or B) = P(A) + P(B) - P(A and B).