5.3 theorems on probability
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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.
5.3 theorems on probability
- 1. www.sanjivanimba.org.in 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. www.sanjivanimba.org.in 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. www.sanjivanimba.org.in NETWORK ANALYSIS At the End of the Session Student will be able to understand- A. Theorems on Probability
- 4. www.sanjivanimba.org.in 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. www.sanjivanimba.org.in 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
- 6. www.sanjivanimba.org.in 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. www.sanjivanimba.org.in EXERCISE List down the various theorems on Probability along with its Formula if any.
- 8. www.sanjivanimba.org.in For More Details Contact Dr. V M Tidake tidkevishal@gmail.com tidkevishalmba@sanjivani.org.in