The document discusses theorems on probability presented by Dr. V. M. Tidake. It defines probability terms like union, intersection, and complement of events. It presents the addition theorem which states the probability of events A or B is equal to the probability of A plus the probability of B minus the probability of A and B together. It also presents the compound probability theorem which gives the probability of dependent events A and B as the probability of A times the conditional probability of B given A. The document concludes by asking students to list theorems on probability and their formulas.

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Unit No.5.
PROBABILITY
Presented By:
Dr. V. M. Tidake
Ph. D (Financial Management), MBA(FM), MBA(HRM) BE(Chem)
Dean, EDP & Associate Professor MBA
1
Sanjivani College of Engineering, Kopargaon
Department of MBA
www.sanjivanimba.org.in

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302-DECISION SCIENCE
Unit No.5. Probability
5.3 Theorems on
Probability
Presented By:
Dr. V. M. Tidake
Ph. D (Financial Management), MBA(FM), MBA(HRM) BE(Chem)
Dean EDP & Associate Professor MBA
2
Sanjivani College of Engineering, Kopargaon
Department of MBA
www.sanjivanimba.org.in

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NETWORK ANALYSIS
 At the End of the Session Student will be able to
understand-
A. Theorems on Probability

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Theorems on Probability
• A U B is the event either A or B or both and is also
denoted as A + B.
• A ∩ B is the event both A and B and is also denoted
as AB.
• Not A or A is the event Not A
• A – B is the event A but Not B

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Mathematical Preliminaries
• Factorial Notation:
n! = n × (n-1) × (n-2)…3 × 2×1
Note: 0! = 1
• Permutation:
nPr = n!/(n-r)!
nPn = n!
• Combination:
nCr = n!/r! (n-r)!
Note: nCr = nCn-r
nC1 = n
nCn = nC0 = 1

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Theorem on Probability
Addition Theorem:
P (A or B) = P (A U B) = P (A) + P (B) – P (A ∩ B)
P (A U B U C) = P(A) + P(B) + P(C) – P(A ∩ B) - P(B ∩ C) - P(A ∩ C) +
P(A ∩ B ∩ C)
Compound Probability Theorem:
For Dependent Events-
P(A and B) = P(A ∩ B) = P(A) * P(B/A) = P(B) * P(A/B)

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EXERCISE
 List down the various theorems on Probability along
with its Formula if any.

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For More Details Contact
Dr. V M Tidake
tidkevishal@gmail.com
tidkevishalmba@sanjivani.org.in