{"id":3164,"date":"2021-11-16T02:18:35","date_gmt":"2021-11-16T01:18:35","guid":{"rendered":"https:\/\/vielhuber.de\/?p=3164"},"modified":"2021-11-16T02:45:35","modified_gmt":"2021-11-16T01:45:35","slug":"corona-mathematik","status":"publish","type":"post","link":"https:\/\/vielhuber.de\/blog\/corona-mathematik\/","title":{"rendered":"Corona-Mathematik"},"content":{"rendered":"\n<p>Im <a href=\"https:\/\/www.rki.de\/DE\/Content\/InfAZ\/N\/Neuartiges_Coronavirus\/Situationsberichte\/Wochenbericht\/Wochenbericht_2021-11-11.pdf?__blob=publicationFile\" target=\"_blank\" rel=\"noreferrer noopener\">RKI-Wochenbericht vom 11.11.2021<\/a> ist auf S. 22 aufgef\u00fchrt, dass \\(36\\%\\) der \u00fcber 60-j\u00e4hrigen Corona-Patienten auf der Intensivstation bereits vollst\u00e4ndig geimpft waren. In dieser Altersgruppe waren zu diesem Zeitpunkt \\(87\\%\\) vollst\u00e4ndig geimpft (siehe S. 18).<\/p>\n\n\n\n<!--more-->\n\n\n\n<p>Sei:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(G\\): \u00dc60-J\u00e4hriger ist geimpft<\/li><li>\\(U\\): \u00dc60-J\u00e4hriger ist ungeimpft<\/li><li>\\(I\\): \u00dc60-J\u00e4hriger ist auf Intensivstation<\/li><\/ul>\n\n\n\n<p>Nun ist<\/p>\n\n\n\n<p>$$P(G) = 0,87 \\wedge P(U) = 0,13.$$<\/p>\n\n\n\n<p>Au\u00dferdem ist<\/p>\n\n\n\n<p>$$P(G|I) = \\frac{P(G \\cap I)}{P(I)} = 0,36 \\wedge P(U|I) = \\frac{P(U \\cap I)}{P(I)} = 0,64.$$<\/p>\n\n\n\n<p>Damit ist<\/p>\n\n\n\n<p>$$P(G \\cap I) = 0,36 \\cdot P(I) \\wedge P(U \\cap I) = 0,64 \\cdot P(I)$$<\/p>\n\n\n\n<p>und wegen<\/p>\n\n\n\n<p>$$P(I|U) = \\frac{P(I \\cap U)}{P(U)} = \\frac{P(U \\cap I)}{P(U)} =  \\frac{0,64 \\cdot P(I)}{0,13} \\Rightarrow P(I) = \\frac{0,13 \\cdot P(I|U)}{0,64}.$$<\/p>\n\n\n\n<p>Daraus folgt<\/p>\n\n\n\n<p>$$P(I|G) = \\frac{P(I \\cap G)}{P(G)} = \\frac{P(G \\cap I)}{P(G)} = \\frac{0,36 \\cdot P(I)}{0,87} = \\frac{0,36 \\cdot \\frac{0,13 \\cdot P(I|U)}{0,64}}{0,87} = \\frac{0,36 \\cdot 0,13}{0,64 \\cdot 0,87} \\cdot P(I|U) \\approx 0,08 \\cdot P(I|U).$$<\/p>\n\n\n\n<p>Damit ist das Risiko der \u00fcber 60-J\u00e4hrigen mit Corona auf der Intensivstation zu landen, f\u00fcr Ungeimpfte mehr als 10x so gro\u00df wie f\u00fcr Geimpfte.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Im RKI-Wochenbericht vom 11.11.2021 ist auf S. 22 aufgef\u00fchrt, dass \\(36\\%\\) der \u00fcber 60-j\u00e4hrigen Corona-Patienten auf der Intensivstation bereits vollst\u00e4ndig geimpft waren. In dieser Altersgruppe waren zu diesem Zeitpunkt \\(87\\%\\) vollst\u00e4ndig geimpft (siehe S. 18).<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"gtbabel_prevent_lngs":"","gtbabel_alt_lng":"","footnotes":""},"categories":[1],"tags":[],"class_list":{"0":"post-3164","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-blog"},"acf":[],"yoast_head":"<title>Corona-Mathematik &#060; Vielhuber David<\/title>\n<meta name=\"description\" content=\"Im RKI-Wochenbericht vom 11.11.2021 ist auf S. 22 aufgef\u00fchrt, dass (36%) der \u00fcber 60-j\u00e4hrigen Corona-Patienten auf der Intensivstation bereits\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/vielhuber.de\/blog\/corona-mathematik\/\" \/>\n<meta property=\"og:locale\" content=\"de_DE\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Corona-Mathematik &#060; 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