1. © 2006 Baylor University Slide 1 Fundamentals of Engineering Analysis EGR 1302 Unit 4, Lecture F Approximate Running Time is 21 Minutes Distance Learning / Online Instructional Presentation Presented by Department of Mechanical Engineering Baylor University Procedures: 1.Select “Slide Show” with the menu: Slide Show|View Show (F5 key), and hit “Enter” 2.You will hear “CHIMES” at the completion of the audio portion of each slide; hit the “Enter” key, or the “Page Down” key, or “Left Click” 3.You may exit the slide show at any time with the “Esc” key; and you may select and replay any slide, by navigating with the “Page Up/Down” keys, and then hitting “Shift+F5”.

2. © 2006 Baylor University Slide 2 Probability Theory A Theory to analyze random events. Applicable to analyzing real-world engineering processes. Deterministic vs. Stochastic 2-body problem Probability theory can be used in the prediction of events.

3. © 2006 Baylor University Slide 3 Use of Probability Theory wind many trials x x x x x x x x x x x Aluminum; e.g. 7075T6 - Tensile Strength? The strength of aluminum is determined by many tests, not theory.

4. © 2006 Baylor University Slide 4 Definition of Probability Theory The probability of an event occurring based on an infinite number of trials. Sample Space = all possible outcomes during the trials. Event result: The number of occurrences of a defined event among all the outcomes of the trials. 1 2 3 4 5 6 x x x x x x Not enough trials!

5. © 2006 Baylor University Slide 5 The Probability of Events from Dice 6 sides is 6 N = 6 1 = 6 possible outcomes 2 coins = 2 2 = 4 possible outcomes

6. © 2006 Baylor University Slide 6 The Sample Space of Two Dice Die123456 1234567 2345678 3456789 45678910 56789 11 6789101112 2 Dice is 6 N = 6 2 = 36 possible outcomes The roll of 2 Dice gives 36 unique events. The game of Craps: On the first roll, a 7 or an 11 wins. A 6 on the first roll; to win must roll a 6 before a 7.

7. © 2006 Baylor University Slide 7 This concludes Unit 4, Lecture F