.. title: Engineering Probability Class 4 Thurs 2021-02-04 .. slug: class04 .. date: 2021-02-04 .. tags: class .. link: .. description: .. type: text .. has_math: true .. sectnum:: .. contents:: Table of contents:: .. Our various computer systems don't talk to each other ----------------------------------------------------- Everyone in this class should-- #. be in gradescope, #. have received an invitation to webex meet for the lectures, #. be reading the messages in webex (formerly called webex teams), #. be in LMS, #. be reading this blog. If you're not in gradescope or webex or webex meet, e.g. because you added late, tell WRF. Probability in the real world - enrichment ------------------------------------------ `Statistician Cracks Code For Lottery Tickets `_ Finding these stories is just too easy. Chapter 2 ctd ------------- #. Today: **counting methods**, Leon-Garcia section 2.3, page 41. a. We have an urn with n balls. #. Maybe the balls are all different, maybe not. #. W/o looking, we take k balls out and look at them. #. Maybe we put each ball back after looking at it, maybe not. #. Suppose we took out one white and one green ball. Maybe we care about their order, so that's a different case from green then white, maybe not. #. Applications: a. How many ways can we divide a class of 12 students into 2 groups of 6? #. How many ways can we pick 4 teams of 6 students from a class of 88 students (leaving 64 students behind)? #. We pick 5 cards from a deck. What's the probability that they're all the same suit? #. We're picking teams of 12 students, but now the order matters since they're playing baseball and that's the batting order. #. We have 100 widgets; 10 are bad. We pick 5 widgets. What's the probability that none are bad? Exactly 1? More than 3? #. In the *approval voting* scheme, you mark as many candidates as you please. The candidate with the most votes wins. How many different ways can you mark the ballot? #. In *preferential voting*, you mark as many candidates as you please, but rank them 1,2,3,... How many different ways can you mark the ballot? To watch -------- Rich Radke's Probability Bites: 9. The Total Probability Theorem 10. Bayes' Rule 11. A Medical Testing Example https://www.youtube.com/playlist?list=PLuh62Q4Sv7BXkeKW4J_2WQBlYhKs_k-pj Xkcd comic ---------- `Correlation `_ Future homework format ---------------------- Instead of having a big homework every week, we'll have smaller homeworks after every class, due in several days. The total work will be the same, but this will test you on the material more quickly. The questions will generally be multiple choice.