PPT-Chapter 2 - Probability

21 Probability Experiments Roll of a Die Frequency Number Rolled A six sided die was rolled repeatedly to determine if there was a tendency for one number to be rolled more than the others The results are displayed in the graph below. And 57375en 57375ere Were None meets the standard for Range of Reading and Level of Text Complexity for grade 8 Its structure pacing and universal appeal make it an appropriate reading choice for reluctant readers 57375e book also o57373ers students Section 2.3. Definition of Probability. Jiaping. Wang. Department of Mathematical Science . 01/16/2013, Wednesday. Outline. . Introduction. . . Definition of Probability. . . Inclusive-Exclusive Principle. Probability Terminology. Classical Interpretation. : Notion of probability based on equal likelihood of individual possibilities (coin toss has 1/2 chance of Heads, card draw has 4/52 chance of an Ace). Origins in games of chance.. 3.1 . The Concept of Probability. 3.2 . Sample Spaces and Events. 3.3 . Some Elementary Probability Rules. 3.4 . Conditional Probability and Independence. 3.5 . Bayes’ Theorem. 3-. 2. Probability Concepts. 4. Introduction. (slide 1 of 3). A key . aspect of solving real business problems is dealing appropriately with uncertainty.. This involves recognizing explicitly that uncertainty exists and using quantitative methods to model uncertainty.. What we learned last class…. We are not good at recognizing/dealing with randomness. Our “random” coin flip results weren’t streaky enough.. If B/G results behave like independent coin flips, we know how many families to EXPECT with 0,1,2,3,4 girls.. Conditional Probability. Conditional Probability: . A probability where a certain prerequisite condition has already been met.. Conditional Probability Notation. The probability of Event A, given that Event B has already occurred, is expressed as P(A | B).. Section 5.1. Randomness, Probability, and Simulation. HAPPY HALLOWEEN!!!!!!. Example 1: . When you toss a coin, there are only two possible outcomes, heads or tails. The figure below on the left shows the results of tossing a coin 20 times. For each number of tosses from 1 to 20, we have plotted the proportion of those tosses that gave a head. You can see that the proportion of heads starts at 1 on the first toss, falls to 0.5 when the second toss gives a tail, then rises to 0.67, and then falls to 0.5, and 0.4 as we get two more tails. After that, the proportion of heads continues to fluctuate but never exceeds 0.5 again.. Sixth Edition. Douglas C. Montgomery George C. . Runger. Chapter 2 Title and Outline. 2. 2. Probability. 2-1 Sample Spaces and Events . 2-1.1 Random Experiments. 2-1.2 Sample Spaces . Continuous Probability Distribution . (pdf) . Definition:. . b. P(a . . X.  . b) = .  . f(x). dx. . . a. For continuous RV X & a. .  b.. Chapter 4: Probability: The Study of Randomness Lecture Presentation Slides Macmillan Learning © 2017 Chapter 4 Probability: The Study of Randomness 4.1 Randomness 4.2 Probability Models 4.3 Random Variables Probability and Probability Distribution Dr Manoj Kumar Bhambu GCCBA-42, Chandigarh M- +91-988-823-7733 mkbhambu@hotmail.com Probability and Probability Distribution: Definitions- Probability Rules –Application of Probability calculus. 1 ≥ . Pr. (h) ≥ 0. If e deductively implies h, then Pr(h|e) = 1. .. (disjunction rule) If h and g are mutually exclusive, then . Pr. (h or g) = . Pr. (h) + . Pr. (g). (disjunction rule) If h and g are . 4. Compute the number of combinations of . n. individuals taken . k. at a time.. Use . combinations to calculate probabilities.. Use . the multiplication counting principle and combinations to calculate probabilities..