PPT-11.1 – Probability – Basic Concepts

Probability The study of the occurrence of random events or phenomena It does not deal with guarantees but with the likelihood of an occurrence of an event Experiment Any observation or measurement of a random phenomenon. Aditya. G. . Parameswaran. Stanford University. Joint work with: . Hector Garcia-Molina (Stanford) and . Anand. . Rajaraman. (. Kosmix. Corp.). . 1. Motivating Examples. tax assessors san . antonio. Aditya. G. . Parameswaran. Stanford University. Joint work with: . Hector Garcia-Molina (Stanford) and . Anand. . Rajaraman. (. Kosmix. Corp.). . 1. Motivating Examples. tax assessors san . antonio. How . can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects . of reality. Albert Einstein. Some parts of these slides were prepared based on . Purpose of Copyright Law. To promote the Progress of Science and useful Arts. by securing for . limited Times . to Authors and Inventors the exclusive Right to their respective Writings and Discoveries.” (U.S. Constitution, Article 1, Section 8 (1789): . 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 . 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.. 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).. One-Part Tasks. The results for simple, one-part tasks can often be listed easily. . Tossing a fair coin:. Rolling a single fair die. Heads. or . tails. 1, 2, 3, 4, 5, 6. Consider a club . N. with four members:. 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 . 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 . How . can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects . of reality. Albert Einstein. Some parts of these slides were prepared based on . 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..