{"id":4905,"date":"2014-07-03T15:08:28","date_gmt":"2014-07-03T06:08:28","guid":{"rendered":"http:\/\/test6.eigoban.jp\/?page_id=4905"},"modified":"2017-11-17T11:53:59","modified_gmt":"2017-11-17T02:53:59","slug":"p-3","status":"publish","type":"page","link":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/probability\/p-3\/","title":{"rendered":"3. Conditional probability and independent events (1.4 &#8211; 1.5)"},"content":{"rendered":"","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"parent":3839,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"page-lecmov.php","meta":{"footnotes":""},"class_list":["post-4905","page","type-page","status-publish","hentry"],"acf":[],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.8 - aioseo.com -->\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<link rel=\"canonical\" href=\"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/probability\/p-3\/\" \/>\n\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 4.9.8\" \/>\n\t\t<meta property=\"og:locale\" content=\"ja_JP\" \/>\n\t\t<meta property=\"og:site_name\" content=\"TSUKUBA OCW | University of Tsukuba | TSUKUBA OCW (Opencourseware) is a platform to establish a new interface between the university and society.\" \/>\n\t\t<meta property=\"og:type\" content=\"article\" \/>\n\t\t<meta property=\"og:title\" content=\"3. Conditional probability and independent events (1.4 \u2013 1.5) | TSUKUBA OCW | University of Tsukuba\" \/>\n\t\t<meta property=\"og:url\" content=\"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/probability\/p-3\/\" \/>\n\t\t<meta property=\"og:image\" content=\"https:\/\/ocw.tsukuba.ac.jp\/en\/wp-content\/uploads\/2022\/10\/ogp.png\" \/>\n\t\t<meta property=\"og:image:secure_url\" content=\"https:\/\/ocw.tsukuba.ac.jp\/en\/wp-content\/uploads\/2022\/10\/ogp.png\" \/>\n\t\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t\t<meta property=\"og:image:height\" content=\"630\" \/>\n\t\t<meta property=\"article:published_time\" content=\"2014-07-03T06:08:28+00:00\" \/>\n\t\t<meta property=\"article:modified_time\" content=\"2017-11-17T02:53:59+00:00\" \/>\n\t\t<meta name=\"twitter:card\" content=\"summary\" \/>\n\t\t<meta name=\"twitter:title\" content=\"3. Conditional probability and independent events (1.4 \u2013 1.5) | TSUKUBA OCW | University of Tsukuba\" \/>\n\t\t<meta name=\"twitter:image\" content=\"https:\/\/ocw.tsukuba.ac.jp\/en\/wp-content\/uploads\/2022\/10\/ogp.png\" \/>\n\t\t<script type=\"application\/ld+json\" class=\"aioseo-schema\">\n\t\t\t{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/course\\\/math\\\/probability\\\/p-3\\\/#breadcrumblist\",\"itemListElement\":[{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en#listItem\",\"position\":1,\"name\":\"\\u30db\\u30fc\\u30e0\",\"item\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\",\"nextItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/course\\\/#listItem\",\"name\":\"Courses\"}},{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/course\\\/#listItem\",\"position\":2,\"name\":\"Courses\",\"item\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/course\\\/\",\"nextItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/course\\\/math\\\/#listItem\",\"name\":\"Mathematics\"},\"previousItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en#listItem\",\"name\":\"\\u30db\\u30fc\\u30e0\"}},{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/course\\\/math\\\/#listItem\",\"position\":3,\"name\":\"Mathematics\",\"item\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/course\\\/math\\\/\",\"nextItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/course\\\/math\\\/probability\\\/#listItem\",\"name\":\"Probability theory\"},\"previousItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/course\\\/#listItem\",\"name\":\"Courses\"}},{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/course\\\/math\\\/probability\\\/#listItem\",\"position\":4,\"name\":\"Probability theory\",\"item\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/course\\\/math\\\/probability\\\/\",\"nextItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/course\\\/math\\\/probability\\\/p-3\\\/#listItem\",\"name\":\"3. Conditional probability and independent events (1.4 &#8211; 1.5)\"},\"previousItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/course\\\/math\\\/#listItem\",\"name\":\"Mathematics\"}},{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/course\\\/math\\\/probability\\\/p-3\\\/#listItem\",\"position\":5,\"name\":\"3. Conditional probability and independent events (1.4 &#8211; 1.5)\",\"previousItem\":{\"@type\":\"ListItem\",\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/course\\\/math\\\/probability\\\/#listItem\",\"name\":\"Probability theory\"}}]},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/#organization\",\"name\":\"TSUKUBA OCW | University of Tsukuba\",\"description\":\"TSUKUBA OCW (Opencourseware) is a platform to establish a new interface between the university and society.\",\"url\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/course\\\/math\\\/probability\\\/p-3\\\/#webpage\",\"url\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/course\\\/math\\\/probability\\\/p-3\\\/\",\"name\":\"3. Conditional probability and independent events (1.4 \\u2013 1.5) | TSUKUBA OCW | University of Tsukuba\",\"inLanguage\":\"ja\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/#website\"},\"breadcrumb\":{\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/course\\\/math\\\/probability\\\/p-3\\\/#breadcrumblist\"},\"datePublished\":\"2014-07-03T15:08:28+09:00\",\"dateModified\":\"2017-11-17T11:53:59+09:00\"},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/#website\",\"url\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/\",\"name\":\"TSUKUBA OCW | University of Tsukuba\",\"description\":\"TSUKUBA OCW (Opencourseware) is a platform to establish a new interface between the university and society.\",\"inLanguage\":\"ja\",\"publisher\":{\"@id\":\"https:\\\/\\\/ocw.tsukuba.ac.jp\\\/en\\\/#organization\"}}]}\n\t\t<\/script>\n\t\t<!-- All in One SEO -->\n\n","aioseo_head_json":{"title":"3. Conditional probability and independent events (1.4 \u2013 1.5) | TSUKUBA OCW | University of Tsukuba","description":"","canonical_url":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/probability\/p-3\/","robots":"max-image-preview:large","keywords":"","webmasterTools":{"miscellaneous":""},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"BreadcrumbList","@id":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/probability\/p-3\/#breadcrumblist","itemListElement":[{"@type":"ListItem","@id":"https:\/\/ocw.tsukuba.ac.jp\/en#listItem","position":1,"name":"\u30db\u30fc\u30e0","item":"https:\/\/ocw.tsukuba.ac.jp\/en","nextItem":{"@type":"ListItem","@id":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/#listItem","name":"Courses"}},{"@type":"ListItem","@id":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/#listItem","position":2,"name":"Courses","item":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/","nextItem":{"@type":"ListItem","@id":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/#listItem","name":"Mathematics"},"previousItem":{"@type":"ListItem","@id":"https:\/\/ocw.tsukuba.ac.jp\/en#listItem","name":"\u30db\u30fc\u30e0"}},{"@type":"ListItem","@id":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/#listItem","position":3,"name":"Mathematics","item":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/","nextItem":{"@type":"ListItem","@id":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/probability\/#listItem","name":"Probability theory"},"previousItem":{"@type":"ListItem","@id":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/#listItem","name":"Courses"}},{"@type":"ListItem","@id":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/probability\/#listItem","position":4,"name":"Probability theory","item":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/probability\/","nextItem":{"@type":"ListItem","@id":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/probability\/p-3\/#listItem","name":"3. Conditional probability and independent events (1.4 &#8211; 1.5)"},"previousItem":{"@type":"ListItem","@id":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/#listItem","name":"Mathematics"}},{"@type":"ListItem","@id":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/probability\/p-3\/#listItem","position":5,"name":"3. Conditional probability and independent events (1.4 &#8211; 1.5)","previousItem":{"@type":"ListItem","@id":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/probability\/#listItem","name":"Probability theory"}}]},{"@type":"Organization","@id":"https:\/\/ocw.tsukuba.ac.jp\/en\/#organization","name":"TSUKUBA OCW | University of Tsukuba","description":"TSUKUBA OCW (Opencourseware) is a platform to establish a new interface between the university and society.","url":"https:\/\/ocw.tsukuba.ac.jp\/en\/"},{"@type":"WebPage","@id":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/probability\/p-3\/#webpage","url":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/probability\/p-3\/","name":"3. Conditional probability and independent events (1.4 \u2013 1.5) | TSUKUBA OCW | University of Tsukuba","inLanguage":"ja","isPartOf":{"@id":"https:\/\/ocw.tsukuba.ac.jp\/en\/#website"},"breadcrumb":{"@id":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/probability\/p-3\/#breadcrumblist"},"datePublished":"2014-07-03T15:08:28+09:00","dateModified":"2017-11-17T11:53:59+09:00"},{"@type":"WebSite","@id":"https:\/\/ocw.tsukuba.ac.jp\/en\/#website","url":"https:\/\/ocw.tsukuba.ac.jp\/en\/","name":"TSUKUBA OCW | University of Tsukuba","description":"TSUKUBA OCW (Opencourseware) is a platform to establish a new interface between the university and society.","inLanguage":"ja","publisher":{"@id":"https:\/\/ocw.tsukuba.ac.jp\/en\/#organization"}}]},"og:locale":"ja_JP","og:site_name":"TSUKUBA OCW | University of Tsukuba | TSUKUBA OCW (Opencourseware) is a platform to establish a new interface between the university and society.","og:type":"article","og:title":"3. Conditional probability and independent events (1.4 \u2013 1.5) | TSUKUBA OCW | University of Tsukuba","og:url":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/probability\/p-3\/","og:image":"https:\/\/ocw.tsukuba.ac.jp\/en\/wp-content\/uploads\/2022\/10\/ogp.png","og:image:secure_url":"https:\/\/ocw.tsukuba.ac.jp\/en\/wp-content\/uploads\/2022\/10\/ogp.png","og:image:width":1200,"og:image:height":630,"article:published_time":"2014-07-03T06:08:28+00:00","article:modified_time":"2017-11-17T02:53:59+00:00","twitter:card":"summary","twitter:title":"3. Conditional probability and independent events (1.4 \u2013 1.5) | TSUKUBA OCW | University of Tsukuba","twitter:image":"https:\/\/ocw.tsukuba.ac.jp\/en\/wp-content\/uploads\/2022\/10\/ogp.png"},"aioseo_meta_data":{"post_id":"4905","title":null,"description":null,"keywords":null,"keyphrases":null,"primary_term":null,"canonical_url":null,"og_title":null,"og_description":null,"og_object_type":"default","og_image_type":"default","og_image_url":null,"og_image_width":null,"og_image_height":null,"og_image_custom_url":null,"og_image_custom_fields":null,"og_video":null,"og_custom_url":null,"og_article_section":null,"og_article_tags":null,"twitter_use_og":false,"twitter_card":"default","twitter_image_type":"default","twitter_image_url":null,"twitter_image_custom_url":null,"twitter_image_custom_fields":null,"twitter_title":null,"twitter_description":null,"schema":{"blockGraphs":[],"customGraphs":[],"default":{"data":{"Article":[],"Course":[],"Dataset":[],"FAQPage":[],"Movie":[],"Person":[],"Product":[],"ProductReview":[],"Car":[],"Recipe":[],"Service":[],"SoftwareApplication":[],"WebPage":[]},"graphName":"","isEnabled":true},"graphs":[]},"schema_type":null,"schema_type_options":null,"pillar_content":false,"robots_default":true,"robots_noindex":false,"robots_noarchive":false,"robots_nosnippet":false,"robots_nofollow":false,"robots_noimageindex":false,"robots_noodp":false,"robots_notranslate":false,"robots_max_snippet":null,"robots_max_videopreview":null,"robots_max_imagepreview":"large","priority":null,"frequency":null,"local_seo":null,"breadcrumb_settings":null,"limit_modified_date":false,"ai":null,"created":"2021-06-29 01:50:47","updated":"2025-06-17 07:12:24","seo_analyzer_scan_date":null},"aioseo_breadcrumb":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\t\t\t<a href=\"https:\/\/ocw.tsukuba.ac.jp\/en\" title=\"\u30db\u30fc\u30e0\">\u30db\u30fc\u30e0<\/a>\n\t\t<\/span><span class=\"aioseo-breadcrumb-separator\">&raquo;<\/span><span class=\"aioseo-breadcrumb\">\n\t\t\t<a href=\"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/\" title=\"Courses\">Courses<\/a>\n\t\t<\/span><span class=\"aioseo-breadcrumb-separator\">&raquo;<\/span><span class=\"aioseo-breadcrumb\">\n\t\t\t<a href=\"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/\" title=\"Mathematics\">Mathematics<\/a>\n\t\t<\/span><span class=\"aioseo-breadcrumb-separator\">&raquo;<\/span><span class=\"aioseo-breadcrumb\">\n\t\t\t<a href=\"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/probability\/\" title=\"Probability theory\">Probability theory<\/a>\n\t\t<\/span><span class=\"aioseo-breadcrumb-separator\">&raquo;<\/span><span class=\"aioseo-breadcrumb\">\n\t\t\t3. Conditional probability and independent events (1.4 \u2013 1.5)\n\t\t<\/span><\/div>","aioseo_breadcrumb_json":[{"label":"\u30db\u30fc\u30e0","link":"https:\/\/ocw.tsukuba.ac.jp\/en"},{"label":"Courses","link":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/"},{"label":"Mathematics","link":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/"},{"label":"Probability theory","link":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/probability\/"},{"label":"3. Conditional probability and independent events (1.4 &#8211; 1.5)","link":"https:\/\/ocw.tsukuba.ac.jp\/en\/course\/math\/probability\/p-3\/"}],"_links":{"self":[{"href":"https:\/\/ocw.tsukuba.ac.jp\/en\/wp-json\/wp\/v2\/pages\/4905","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ocw.tsukuba.ac.jp\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ocw.tsukuba.ac.jp\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ocw.tsukuba.ac.jp\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ocw.tsukuba.ac.jp\/en\/wp-json\/wp\/v2\/comments?post=4905"}],"version-history":[{"count":7,"href":"https:\/\/ocw.tsukuba.ac.jp\/en\/wp-json\/wp\/v2\/pages\/4905\/revisions"}],"predecessor-version":[{"id":6745,"href":"https:\/\/ocw.tsukuba.ac.jp\/en\/wp-json\/wp\/v2\/pages\/4905\/revisions\/6745"}],"up":[{"embeddable":true,"href":"https:\/\/ocw.tsukuba.ac.jp\/en\/wp-json\/wp\/v2\/pages\/3839"}],"wp:attachment":[{"href":"https:\/\/ocw.tsukuba.ac.jp\/en\/wp-json\/wp\/v2\/media?parent=4905"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}