Slide 1Odds…iClicker questions:1st day of NBA Season (10/30/2013)Slide 5Slide 6Chapter 17 – Changed SlidesOdds…•What are the odds?•Related to, but different than probability•Odds range from 0 to infinity, while probability can range from 0 to 1•Want to convert them to probabilities•Odds in terms of 2 numbers: A to B•Odds FOR the outcome•Odds of A to B FOR an outcome means probability of outcome is A / (A + B)•“Odds of 5 to 1 FOR team winning” means A=5 and B=1Probability of the team winning is A / (A + B) = 5 / (5 + 1) = 5/6•That is, “the probability of the team winning is 5/6.”•Odds AGAINST the outcome•Odds of A to B AGAINST an outcome means probability against the outcome is B / (A + B)•“Odds of 5 to 1 AGAINST team winning” means A=5 and B=1Probability of the team winning is B / (A + B) = 1 / (5 + 1) = 1/6•That is, “the probability of the team winning is 1/6.”•If the odds are 18 to 2 against a team winning, then the probability of the team winning is estimated to be:A. 2/16 = 0.125B. 2/18 = 0.111C. 2/20 = 0.100D. 16/18 = 0.889E. 18/20 = 0.900iClicker questions:•If the odds are 18 to 2 for a team winning, then the probability of the team winning is estimated to be:A. 2/16 = 0.125B. 2/18 = 0.111C. 2/20 = 0.100D. 16/18 = 0.889E. 18/20 = 0.900Notes: •Probabilities are intuitive for us to understand – they give us the chances of something happening. •Odds are…..well just the odds. It is a different way to quantify the likelihood of something happening. Odds for team winning are 18 to 2 means A=18 and B=2P(“18 to 2”) = A / (A + B) = 18 / (18 + 2)= 18 / 20 = 0.900 Odds against team winning are 18 to 2 means A=18 and B=2P(“18 to 2”) = B/ (A + B) = 2 / (18 + 2)= 2 / 20 = 0.1001st day of NBA Season (10/30/2013)•Odds against Philadelphia 76ers winning the NBA championship (per odds makers) are 9,999 to 1•According to National Public Radio (NPR) Morning Edition, it was set at that level because that was the biggest number their computers/software could handle…• P(9,999 to 1) = B / (A + B)= (1 / (1 + 9,999) = 1 / 10,000 = 0.00001•http://www.philly.com/philly/sports/20131029_ap_1952e2accc304c9ea641cb52412175c0.htmlChapter 18 – Venn Diagram SlidesA little set theory and Venn diagramsABABACUnion of A and B = everything in A OR BA and B are “disjoint.” That is,they have nothing in common. Intersection of A and B =Everything in A AND
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