{"id":1894,"date":"2019-03-28T12:00:00","date_gmt":"2019-03-28T11:00:00","guid":{"rendered":"https:\/\/kindsonthegenius.com\/blog\/conditional-probability-application-of-bayess-rule\/"},"modified":"2026-07-05T03:22:26","modified_gmt":"2026-07-05T01:22:26","slug":"conditional-probability-application-of-bayess-rule","status":"publish","type":"post","link":"https:\/\/kindsonthegenius.com\/blog\/conditional-probability-application-of-bayess-rule\/","title":{"rendered":"Conditional Probability \u2013 Application of Bayes\u2019s Rule"},"content":{"rendered":"

In the previous lesson(Introduction to Bayes’ Rule<\/a>), we saw how Bayes’ Rule can be applied to medical diagnosis.<\/p>\n

So in this chapter, we would see how Bayes’ Rule applies to interrogation.\u00a0 Let’s take an example.<\/p>\n

 <\/p>\n

\n

The Polygraph Example<\/strong><\/p>\n

A polygraph test ( also called a lie-detector test) is normally administered to crime suspects during investigation.<\/p>\n

Let +<\/strong> denote the event that the polygraph give a positive result (indicating that the suspect is lying)<\/p>\n

Let –<\/strong> denote the event that the polygraph gives a negative result(indicating that that suspect is telling the truth)<\/p>\n

Let T<\/strong> denote the event that the suspect is telling the truth<\/p>\n

Let L<\/strong> denote the event that the suspect is lying<\/p>\n

From studied carried out, it is found out that:<\/p>\n

P(+ | L) = 0.88<\/strong> (meaning that the polygraph detects liars with an accuracy of 88%<\/p>\n

It follows that, P(- | L) = 0.12<\/strong> (this is false negative and follows from P(- | L) = 1 – P(+ | L)<\/p>\n

Also P(- | T) = 0.86 (<\/strong>meaning that the polygraph detects when truth is told with accuracy of 86%<\/p>\n

It also follow that P(+ | T) = 0.14<\/strong> (this is false positive)<\/p>\n

 <\/p>\n

Assuming that on a particular question, almost all suspects have no reason to lie and so P(T) = 0.99. Meaning that P(L) = 0.1.<\/p>\n

If a suspect produces a positive test result on the polygraph. What is the probability that the the this is a false positive (the polygraph is incorrect) and the suspect is telling the truth?<\/p>\n

\n

This can be evaluated using Bayes’ Rule<\/p>\n

\"Result<\/p>\n

Interpretation<\/strong><\/p>\n

This means that there is 94% chance that the polygraph is incorrect. Or 94% of the persons who are detected as lying were actually telling the truth.<\/p>\n

This is why the results of Polygraph tests are not admissible in court. They are only used to assist the investigation process.<\/p>\n","protected":false},"excerpt":{"rendered":"

In the previous lesson(Introduction to Bayes’ Rule), we saw how Bayes’ Rule can be applied to medical diagnosis. So in this chapter, we would see … <\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"pagelayer_contact_templates":[],"_pagelayer_content":"","footnotes":""},"categories":[414],"tags":[],"class_list":["post-1894","post","type-post","status-publish","format-standard","hentry","category-programming"],"_links":{"self":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/1894","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/comments?post=1894"}],"version-history":[{"count":1,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/1894\/revisions"}],"predecessor-version":[{"id":2062,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/posts\/1894\/revisions\/2062"}],"wp:attachment":[{"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/media?parent=1894"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/categories?post=1894"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kindsonthegenius.com\/blog\/wp-json\/wp\/v2\/tags?post=1894"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}