# Lec04 - 2.2 Additive Rule of Probability IOE/Mfg/Stats 265,...

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1 IOE/Mfg/Stats 265, Win 2009 Lecture #4: Conditioning and Independence More Learning Outcomes: 5. Calculate and interpret conditional probabilities . 6. Determine independence of events and use to calculate probabilities. 7. Use Bayes’ Theorem to calculate conditional probabilities 2 2.2 Additive Rule of Probability A B () ( ) ( ) PA B PA PB ! " # \$ 3 Example 1: Credit Cards Prob Student has Visa Card = 0.50 Prob Students have MC = 0.40 Prob Students have Both Cards = 0.25. What is the probability that a student does not have a MC? What is the probability that a student has neither card? (Draw a Venn Diagram) 6 Example 2: Extrusion Die Alum Rods (revisited from Lec03) Diameter Length Too Thin OK Too Thick Too Short 10 3 5 OK 38 900 4 Too Long 2 25 13 Confirm the Addition Rule for these data …

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7 Example 2: (continued) Let P(A) = Prob (part diameter is O.K.) Let P(B) = Prob (part length is O.K.) Based on a random sample, estimate P(A) = P(B) = P(A \$ B) = P(A B) = 9 9 Example 3: Additive Rule for 3 Events Given 3 Events A, B, and C What is the probability that event A and B will occur? What is the probability that event A and B and C will occur? () ( ) ( ) ( ) PA B C PA PB PC PA B PA C PB C ! " " #\$ # \$ # \$ "\$ \$ ( ) 0.70 ( ) 0.80 ( ) 0.75 ( ) 0.85 ( ) 0.55 ( ) 0.60 0 . 9 ? 8 ? PA PB ! ! ! ! \$! ! C B A 11 Mutually Exclusive (Disjoint ) Events Two events are mutually exclusive (disjoint) if A \$ B = Ø that is A and B have no elements in common. If A and B are mutually exclusive, then: Draw a Venn Diagram that depicts two mutually exclusive events. %& % & % & ! " 12 Addition Rules for Mutually Exclusive Events
13 Example 4: Voting 35% of Democratic primary voters chose Clinton

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## This note was uploaded on 03/17/2010 for the course IOE 265 taught by Professor Garyherrin during the Fall '09 term at University of Michigan-Dearborn.

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Lec04 - 2.2 Additive Rule of Probability IOE/Mfg/Stats 265,...

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