{"id":43416,"date":"2024-04-15T21:29:07","date_gmt":"2024-04-15T21:29:07","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=43416"},"modified":"2024-04-15T21:29:07","modified_gmt":"2024-04-15T21:29:07","slug":"bayes-theorem-is-given-by-where-1-ph-is-the-probability-of-hypothesis-h-being-true-2-pe-is-the-probability-of-the-evidenceregardless-of-the-hypothesis-3-peh-is-the-probability-of-the-evi","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/bayes-theorem-is-given-by-where-1-ph-is-the-probability-of-hypothesis-h-being-true-2-pe-is-the-probability-of-the-evidenceregardless-of-the-hypothesis-3-peh-is-the-probability-of-the-evi\/","title":{"rendered":"Bayes Theorem is given by where 1. P(H) is the probability of hypothesis H being true. 2. P(E) is the probability of the evidence(regardless of the hypothesis). 3. P(E|H) is the probability of the evidence given that hypothesis is true. 4. P(H|E) is the probability of the hypothesis given that the evidence is there."},"content":{"rendered":"<p>[amp_mcq option1=&#8221;TRUE&#8221; option2=&#8221;nan&#8221; option3=&#8221;nan&#8221; option4=&#8221;nan&#8221; correct=&#8221;option1&#8243;]<!--more--><\/p>\n<p>The correct answer is: TRUE.<\/p>\n<p>Bayes&#8217; theorem is a mathematical formula that is used to calculate the probability of a hypothesis being true given some evidence. The theorem is named after Thomas Bayes, an English mathematician who first published it in 1763.<\/p>\n<p>Bayes&#8217; theorem can be written as follows:<\/p>\n<p>$$P(H|E) = \\frac{P(E|H)P(H)}{P(E)}$$<\/p>\n<p>where:<\/p>\n<ul>\n<li>$P(H|E)$ is the probability of hypothesis $H$ being true given evidence $E$.<\/li>\n<li>$P(E|H)$ is the probability of evidence $E$ given hypothesis $H$.<\/li>\n<li>$P(H)$ is the probability of hypothesis $H$ being true.<\/li>\n<li>$P(E)$ is the probability of evidence $E$.<\/li>\n<\/ul>\n<p>Bayes&#8217; theorem can be used to calculate the probability of a hypothesis being true given some evidence. For example, if we know that the probability of a person having a certain disease is 0.1, and we know that the probability of a person with that disease having a certain symptom is 0.9, then we can use Bayes&#8217; theorem to calculate the probability that a person with that symptom has the disease.<\/p>\n<p>Bayes&#8217; theorem can also be used to update our beliefs about a hypothesis as we receive new evidence. For example, if we initially believe that the probability of a hypothesis being true is 0.5, and we then receive evidence that makes the hypothesis more likely, we can use Bayes&#8217; theorem to update our belief to a higher probability.<\/p>\n<p>Bayes&#8217; theorem is a powerful tool that can be used to make inferences about the world around us. It is used in a variety of fields, including statistics, machine learning, and decision analysis.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[amp_mcq option1=&#8221;TRUE&#8221; option2=&#8221;nan&#8221; option3=&#8221;nan&#8221; option4=&#8221;nan&#8221; correct=&#8221;option1&#8243;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[729],"tags":[],"class_list":["post-43416","post","type-post","status-publish","format-standard","hentry","category-machine-learning","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Bayes Theorem is given by where 1. P(H) is the probability of hypothesis H being true. 2. P(E) is the probability of the evidence(regardless of the hypothesis). 3. P(E|H) is the probability of the evidence given that hypothesis is true. 4. P(H|E) is the probability of the hypothesis given that the evidence is there.<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/bayes-theorem-is-given-by-where-1-ph-is-the-probability-of-hypothesis-h-being-true-2-pe-is-the-probability-of-the-evidenceregardless-of-the-hypothesis-3-peh-is-the-probability-of-the-evi\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Bayes Theorem is given by where 1. P(H) is the probability of hypothesis H being true. 2. P(E) is the probability of the evidence(regardless of the hypothesis). 3. P(E|H) is the probability of the evidence given that hypothesis is true. 4. 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