{"id":183,"date":"2019-11-25T03:20:12","date_gmt":"2019-11-25T03:20:12","guid":{"rendered":"http:\/\/blog.newtonchineseschool.org\/lilijia\/?p=183"},"modified":"2019-11-26T04:14:50","modified_gmt":"2019-11-26T04:14:50","slug":"aops_cp-week-11-geometric-probability","status":"publish","type":"post","link":"https:\/\/blog.newtonchineseschool.org\/lilijia\/2019\/11\/25\/aops_cp-week-11-geometric-probability\/","title":{"rendered":"AoPS_CP Week 11: Geometric Probability"},"content":{"rendered":"\n<p><strong>Lesson Review:<\/strong><\/p>\n\n\n\n<p>Geometric Probability can be used in situations where we don\u2019t have a set of individual items to count; rather, we have infinitely many outcomes which can be nicely represented using some geometric object (a line segment, a region of a plane, etc). Or say, we use geometric probability when our outcomes are <strong>continuous<\/strong> rather than <strong>discrete<\/strong>. <\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/11\/line.png\" alt=\"\" class=\"wp-image-185\" width=\"289\" height=\"128\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/11\/line.png 412w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/11\/line-300x133.png 300w\" sizes=\"(max-width: 289px) 100vw, 289px\" \/><\/figure>\n\n\n\n<p>We learned probability using <strong>lengths<\/strong> and <strong>areas<\/strong>. (In the future, you may meet some problems that require <strong>volumes<\/strong>.)<\/p>\n\n\n\n<p><strong>P (success) = Size of successful region\/size of possible region<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" src=\"http:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/11\/GeometricProbability.jpg\" alt=\"\" class=\"wp-image-184\" width=\"336\" height=\"252\" srcset=\"https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/11\/GeometricProbability.jpg 960w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/11\/GeometricProbability-300x225.jpg 300w, https:\/\/blog.newtonchineseschool.org\/lilijia\/files\/2019\/11\/GeometricProbability-768x576.jpg 768w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><figcaption>There are 3 types of geometric probabilities, one for each of the commonly used dimensions of space; length, area and volume. Target length. 1D. P(Target) = Total length. Target area. 2D. P(Target) = Total area. Target volume. 3D. P(Target) = Total volume.<\/figcaption><\/figure>\n\n\n\n<p><strong>Homework:<\/strong> <\/p>\n\n\n\n<ul><li>P156 Ex. 10.2.1, 10.2.3, 10.2.5<\/li><li>P161 Ex 10.3.1-10.3.4<\/li><li>Bonus: P162 Ex 10.7, P163 Ex 10.16<\/li><\/ul>\n\n\n\n<p><strong>Other Resources:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Geometric Probability\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/8P6HGcwQYZ0?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p><a href=\"https:\/\/www.khanacademy.org\/math\/ap-statistics\/random-variables-ap\/geometric-random-variable\/e\/geometric-probability\">https:\/\/www.khanacademy.org\/math\/ap-statistics\/random-variables-ap\/geometric-random-variable\/e\/geometric-probability<\/a><\/p>\n\n\n\n<p>*Next Sunday we have no school. Wish everyone a great Thanksgiving holiday! See you on 12\/08!<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Lesson Review: Geometric Probability can be used in situations where we don\u2019t have a set of individual items to count; rather, we have infinitely many outcomes which can be nicely represented using some geometric object (a line segment, a region of a plane, etc). Or say, we use geometric probability when our outcomes are continuous [&hellip;]<\/p>\n","protected":false},"author":157,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/183"}],"collection":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/users\/157"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/comments?post=183"}],"version-history":[{"count":3,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/183\/revisions"}],"predecessor-version":[{"id":199,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/posts\/183\/revisions\/199"}],"wp:attachment":[{"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/media?parent=183"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/categories?post=183"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.newtonchineseschool.org\/lilijia\/wp-json\/wp\/v2\/tags?post=183"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}