{"id":11301,"date":"2021-05-20T09:35:17","date_gmt":"2021-05-20T09:35:17","guid":{"rendered":"http:\/\/www.max-sperling.bplaced.net\/?p=11301"},"modified":"2021-05-20T09:35:17","modified_gmt":"2021-05-20T09:35:17","slug":"stochastic-example-1","status":"publish","type":"post","link":"http:\/\/www.max-sperling.bplaced.net\/?p=11301","title":{"rendered":"Math &#8211; Exercise 3 (Stochastic)"},"content":{"rendered":"<p><strong>Given<\/strong><br \/>\n<center>Two dice (cubes, 6 faces, 1 to 6) are getting rolled.<\/center><\/p>\n<hr>\n<p><strong>Find<\/strong><br \/>\n<center>The probability that the sum is smaller then 5 or greater then 8.<\/center><\/p>\n<hr>\n<p><strong>Solution<\/strong><br \/>\n<center><br \/>\n\\(<br \/>\n\\begin{array}{l}<br \/>\n  \\text{The sample space:} \\\\<br \/>\n  \\begin{align*}<br \/>\n    S = \\{&#038;(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), \\\\<br \/>\n          &#038;(2,1), (2,2), (2,3), (2,4), (2,5), (2,6), \\\\<br \/>\n          &#038;(3,1), (3,2), (3,3), (3,4), (3,5), (3,6), \\\\<br \/>\n          &#038;(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), \\\\<br \/>\n          &#038;(5,1), (5,2), (5,3), (5,4), (5,5), (5,6), \\\\<br \/>\n          &#038;(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)\\}<br \/>\n  \\end{align*} \\\\\\\\<br \/>\n  \\text{The event spaces:} \\\\<br \/>\n  E_{<5} = \\{(1,1), (1,2), (1,3), (2,1), (2,2), (3,1)\\} \\\\\n  E_{>8} = \\{(3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6)\\} \\\\\\\\<br \/>\n  \\text{The event probability:} \\\\<br \/>\n  P(E_{<5} \\bigcup E_{>8}) = \\frac{N(E_{<5})+N(E_{>8})}{N(S)} = \\frac{16}{36} = \\frac{4}{9}<br \/>\n\\end{array}<br \/>\n\\)<br \/>\n<\/center><\/p>\n<hr>\n<p><strong>Answer<\/strong><br \/>\n<center>\\(P(E_{<5} \\bigcup E_{>8}) = \\frac{4}{9}\\)<\/center><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Given Two dice (cubes, 6 faces, 1 to 6) are getting rolled. Find The probability that the sum is smaller<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[47],"tags":[],"_links":{"self":[{"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/posts\/11301"}],"collection":[{"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=11301"}],"version-history":[{"count":0,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=\/wp\/v2\/posts\/11301\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11301"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11301"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.max-sperling.bplaced.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11301"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}