5.3 theorems on probability

THEORY ON PROBABILITY

1. 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

2. 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

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

4. 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

5. Mathematical Preliminaries Factorial Notation: n! = n × (n-1) × (n-2)…3 × 2 × 1 Note: 0! = 1 Permutation: n P r = n!/(n-r)! n P n = n! Combination: n C r = n!/r! (n-r)! Note: n C r = n C n -r n C 1 = n n C n = n C = 1

6. 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)

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

8. For More Details Contact Dr. V M Tidake [email protected] [email protected]