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NUGULA SWATI 20220802311
SHUBHAM LADE 20220802312
VEDANT MORE 20220802313
Bayes’ Theorem
ANOTHER
EVENT, IS
EQUAL TO
THE
LIKELIHOO
D OF THE
SECOND
EVENT
GIVEN THE
FIRST
EVENT
MULTIPLIE
D BY THE
PROBABILI
TY OF THE
FIRST
EVENT.
Introduction
Definition • Bayes theorem is a statistical
formula to determine the conditional
probability of an event. It describes
the probability of an event based on
prior knowledge of events that have
already happened. Bayes Theorem
is named after the Reverend
Thomas Bayes .
Formula • Formula of Bayes' Theorem for
random variable :-
Statistics
• Three urns contain 6 red, 4 black; 4 red, 6
black, and 5 red, 5 black balls respectively.
One of the urns is selected at random and
a ball is drawn from it. If the ball drawn is
red, find the probability that it is drawn
from the first urn.
• Bayes Theorem can be derived for
events and random variables
separately using the definition of
conditional probability and density.
E1 = urn first is chosen
E2 = urn second is chosen
E3 = urn third is chosen
A = ball drawn is red
P(E1) = P(E2) = P(E3) =
1/3
P(A/E1) = 6/10
P(A/E2) = 4/10
P(A/E3) = 5/10
P(E1/A) = P(E1) P(A/E1) + P(E2) P(A/E2) +
P(E3) P(A/E3)
= (1/3 * 6/10) + (1/3 * 4/10) + (1/3 * 5/10)
=2/5
Example
Proof
Advantages Disadvantages
• The method provides a principled and natural way
in the estimation of the probability.
• It is very much Flexible and prior data which are
used in this method is realistic.
• It is following the principle of likelihood which is
helpful for the estimation of probability.
• Bayes’ theorem is interpreted probability with the
help of mathematical formula.
• This does not have any correct or particular way
which helps to choose the prior.
• This method produces the posterior distribution by
the influence of the prior information
• Sometimes there needs to be a high compilation
cost to complete the method when there are a large
number of parameters or areas
Applicat
ions
Internet
Marketing
Medical Field
Solving
Puzzles
The Two Child
Problem
The Monty H
Problem
Cancer rate
Drug testing
Three Prisoner
Problem
Decision
Analysis
Decision Trees
• It is concluded that
this study is
discussing Bayes
theorem and its
formula and use in
everyday life. In the
study, this is seen:
“Bayes theorem” is
a mathematical
method that helps
to interpret the
future situation.
• This theory is help
to interpreted the
“Probability” of one
situation by
Conclusion
References
• Chat GPT
• Wikipedia
• First Course in Portability

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Baise theorm.pptx

  • 1. NUGULA SWATI 20220802311 SHUBHAM LADE 20220802312 VEDANT MORE 20220802313 Bayes’ Theorem
  • 2. ANOTHER EVENT, IS EQUAL TO THE LIKELIHOO D OF THE SECOND EVENT GIVEN THE FIRST EVENT MULTIPLIE D BY THE PROBABILI TY OF THE FIRST EVENT. Introduction
  • 3. Definition • Bayes theorem is a statistical formula to determine the conditional probability of an event. It describes the probability of an event based on prior knowledge of events that have already happened. Bayes Theorem is named after the Reverend Thomas Bayes . Formula • Formula of Bayes' Theorem for random variable :- Statistics
  • 4. • Three urns contain 6 red, 4 black; 4 red, 6 black, and 5 red, 5 black balls respectively. One of the urns is selected at random and a ball is drawn from it. If the ball drawn is red, find the probability that it is drawn from the first urn. • Bayes Theorem can be derived for events and random variables separately using the definition of conditional probability and density. E1 = urn first is chosen E2 = urn second is chosen E3 = urn third is chosen A = ball drawn is red P(E1) = P(E2) = P(E3) = 1/3 P(A/E1) = 6/10 P(A/E2) = 4/10 P(A/E3) = 5/10 P(E1/A) = P(E1) P(A/E1) + P(E2) P(A/E2) + P(E3) P(A/E3) = (1/3 * 6/10) + (1/3 * 4/10) + (1/3 * 5/10) =2/5 Example Proof
  • 5. Advantages Disadvantages • The method provides a principled and natural way in the estimation of the probability. • It is very much Flexible and prior data which are used in this method is realistic. • It is following the principle of likelihood which is helpful for the estimation of probability. • Bayes’ theorem is interpreted probability with the help of mathematical formula. • This does not have any correct or particular way which helps to choose the prior. • This method produces the posterior distribution by the influence of the prior information • Sometimes there needs to be a high compilation cost to complete the method when there are a large number of parameters or areas
  • 6. Applicat ions Internet Marketing Medical Field Solving Puzzles The Two Child Problem The Monty H Problem Cancer rate Drug testing Three Prisoner Problem Decision Analysis Decision Trees
  • 7. • It is concluded that this study is discussing Bayes theorem and its formula and use in everyday life. In the study, this is seen: “Bayes theorem” is a mathematical method that helps to interpret the future situation. • This theory is help to interpreted the “Probability” of one situation by Conclusion References • Chat GPT • Wikipedia • First Course in Portability