THEORY ON PROBABILITY

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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