PPT-Introduction to Probability

Assigning Probabilities and Probability Relationships Chapter 4 BA 201 Assigning Probabilities Assigning Probabilities Basic Requirements for Assigning Probabilities 1 The probability assigned to each experimental. T.Jagannadha. . Swamy. Dept of . ECE,Griet. Random Variable. A random variable . x. takes on a defined set of values with different probabilities.. For example, if you roll a die, the outcome is random (not fixed) and there are 6 possible outcomes, each of which occur with probability one-sixth. . QSCI 381 – Lecture 12. (Larson and Farber, Sect 4.1). Learning objectives. Become comfortable with variable definitions. Create and use probability distributions. Random Variables-I. A . Jake Blanchard. Spring 2010. Uncertainty Analysis for Engineers. 1. Introduction. Interpretations of Probability. Classical – If an event can occur in N equally likely and different ways, and if n of these have an attribute A, then the probability of the occurrence of A, denoted Pr(A), is defined as n/N. B. y. Daniel Christie. Probability. In a class of four brunettes, two blondes, and two people with black hair, what is the probability that any given person would be blonde?. 1/4. Venn Diagrams. Tree Diagrams. 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. AMATYC Presentation November 2009. Lance Phillips – Tulsa Community College. The Vocabulary of Probability. Experiment – A situation which involves chance or probability the result of which is called an outcome.. 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.. 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).. A value between zero and one that describe the relative possibility(change or likelihood) an event occurs.. The MEF announces that in 2012 the change Cambodia economic growth rate is equal to 7% is 80%.. What is probability?. Classical definition:. the . ratio. of “favorable” to equally probable . cases. .. “. favorable”. :. . the kind you’re interested . in. .. Probability of getting heads on flipping a fair coin: 1/2 (heads is 1 of 2 possibilities). 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 . Nisheeth. Random Variables. 2. Informally, a random variable (. r.v.. ) . denotes possible outcomes of an event. Can be discrete (i.e., finite many possible outcomes) or continuous. Some examples of discrete . 4. Interpret probability as a long-run relative frequency. . Dispel . common myths about randomness.. Use . simulation to model chance behavior.. Randomness, Probability, and Simulation. Randomness, Probability, and Simulation.