{"id":41349,"date":"2026-09-15T16:05:20","date_gmt":"2026-09-15T16:05:20","guid":{"rendered":"https:\/\/mp.moonpreneur.com\/math-corner\/?p=41349"},"modified":"2026-09-21T17:40:10","modified_gmt":"2026-09-21T17:40:10","slug":"what-is-conditional-probability","status":"publish","type":"post","link":"https:\/\/mp.moonpreneur.com\/math-corner\/what-is-conditional-probability\/","title":{"rendered":"Conditional Probability: Formula, Examples &#038; Easy Explanation"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"41349\" class=\"elementor elementor-41349\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<div class=\"elementor-inner\">\n\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-0737861 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0737861\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4a68f68\" data-id=\"4a68f68\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-145051e elementor-widget elementor-widget-text-editor\" data-id=\"145051e\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">Ever had the question of how the probability of an event will be affected by having prior knowledge about the event? Here comes the application of conditional probability. Conditional probability is used to determine the probability of an event given that another event has taken place.<\/span><\/p><p><span style=\"font-weight: 400;\">For instance, in trying to determine the probability of a student passing in math tests after being made aware of the fact that the student had extra classes, then conditional probability is applied.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-63e64aa elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"63e64aa\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-bd5a6b5\" data-id=\"bd5a6b5\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e869d51 elementor-widget elementor-widget-text-editor\" data-id=\"e869d51\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><strong>What Is Conditional Probability?<\/strong><b><\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-ce99f7e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ce99f7e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-76b5b2b\" data-id=\"76b5b2b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c09b2c0 elementor-widget elementor-widget-text-editor\" data-id=\"c09b2c0\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">The term conditional probability denotes the chances of an event occurring on account of the other event happening beforehand.<\/span><\/p><p><span style=\"font-weight: 400;\">Symbolically, conditional probability is expressed as P(A | B), which conveys that \u201cthe probability of A under the conditions of B.\u201d<\/span><\/p><p><span style=\"font-weight: 400;\">In the above expression:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><strong>A denotes the events we are examining.<\/strong><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><strong>B denotes the event or condition which has already happened.<\/strong><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><strong>P(A | B) implies the probability of A occurring when B has happened.<\/strong><\/li><\/ul><p><span style=\"font-weight: 400;\">It is worth noting that with regard to conditional probability, the available information modifies the circumstances of the case at hand.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-98e9eee elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"98e9eee\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5a296e6\" data-id=\"5a296e6\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-026cdd2 elementor-widget elementor-widget-text-editor\" data-id=\"026cdd2\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><strong>Conditional Probability Calculations<\/strong><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-10cd31e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"10cd31e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-81e92f2\" data-id=\"81e92f2\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-750e4e3 elementor-widget elementor-widget-text-editor\" data-id=\"750e4e3\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">Given the above definition, the calculation of conditional probability is shown by the following formula:<\/span><\/p><p><b>P(A | B) = P(A \u2229 B) \/ P(B)<\/b><\/p><p><span style=\"font-weight: 400;\">Where:<\/span><\/p><p><b>P(A | B) = likelihood of A occurring with knowledge of B<\/b><\/p><p><b>P(A \u2229 B) = likelihood of A and B occurring together<\/b><\/p><p><b>P(B) = likelihood of B<\/b><\/p><p><span style=\"font-weight: 400;\">The formula presupposes that P(B) does not equal 0.<\/span><\/p><p><span style=\"font-weight: 400;\">Therefore, to calculate the conditional probability correctly, one needs to rely on the cases of the occurrence of event B, and see how often event A can happen at the same time.<\/span><\/p><p><strong>Recommended reading: <\/strong><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/properties-of-real-numbers\/\">What are the Properties of Real Numbers?<\/a><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-9fe999a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9fe999a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a022910\" data-id=\"a022910\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a8921a6 elementor-widget elementor-widget-text-editor\" data-id=\"a8921a6\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><b>How to Calculate Conditional Probability<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-5193aba elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5193aba\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a1095c4\" data-id=\"a1095c4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e6401ed elementor-widget elementor-widget-text-editor\" data-id=\"e6401ed\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">You can calculate conditional probability using three simple steps:<\/span><\/p><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><strong>Identify the event you want to find.<\/strong><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><strong>Identify the condition that is already known.<\/strong><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><strong>Use the conditional probability formula.<\/strong><\/li><\/ol>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-bf5648c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bf5648c\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b8b417d\" data-id=\"b8b417d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2f66645 elementor-widget elementor-widget-text-editor\" data-id=\"2f66645\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3 style=\"text-align: center;\"><b>Simple Example<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-3fd52e7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3fd52e7\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5d9c246\" data-id=\"5d9c246\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-35945a9 elementor-widget elementor-widget-text-editor\" data-id=\"35945a9\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">Let\u2019s take an example of a class containing 30 students, where 18 of them are into playing basketball, while out of those 18 students, 10 also play soccer.<\/span><\/p><p><span style=\"font-weight: 400;\">If we know in advance that the student plays basketball, then what would be the probability of him or her playing soccer?<\/span><\/p><p><strong>In this case:<\/strong><\/p><ul><li><span style=\"font-weight: 400;\">Event A = student plays soccer<\/span><\/li><li><span style=\"font-weight: 400;\">Event B = student plays basketball<\/span><\/li><li><span style=\"font-weight: 400;\">Total students playing both sports = 10<\/span><\/li><li><span style=\"font-weight: 400;\">Total students playing basketball = 18<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">Thus,<\/span><\/p><p><strong>P(A|B) = 10\/18 = 5\/9<\/strong><\/p><p><strong>Therefore, P(A|B) = 5\/9 or 55.56%.<\/strong><\/p><p><span style=\"font-weight: 400;\">It is clear from the above example that not all students (i.e., 30) are considered while calculating the probability.<\/span><\/p><p><strong>Conditional Probability in Daily Life<\/strong><\/p><p><span style=\"font-weight: 400;\">The concept of conditional probability is not confined to academic studies only. Conditional probability finds application in various aspects of life and in the professional environment.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-e5c8655 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e5c8655\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a22d308\" data-id=\"a22d308\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-db459c2 elementor-widget elementor-widget-text-editor\" data-id=\"db459c2\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3 style=\"text-align: center;\"><b>Conditional Probability in Real Life<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-bf8b7b8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bf8b7b8\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4d999e5\" data-id=\"4d999e5\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ab9ed1d elementor-widget elementor-widget-text-editor\" data-id=\"ab9ed1d\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<ul><li><b>Weather forecast:<\/b><span style=\"font-weight: 400;\"> Estimation of rain probability considering the atmospheric conditions.<\/span><\/li><li><b>Medical testing:<\/b><span style=\"font-weight: 400;\"> Estimation of the probability of disease for a person based on his\/her test results.<\/span><\/li><li><b>Sports:<\/b><span style=\"font-weight: 400;\"> Estimation of the probability of winning of a team taking into account its present score.<\/span><\/li><li><b>Business: <\/b><span style=\"font-weight: 400;\">Prediction of customers&#8217; actions based on their previous experience.<\/span><\/li><li><b>Insurance: <\/b><span style=\"font-weight: 400;\">Estimation of risks basing on the information about the customers and previous events.<\/span><\/li><li><b>Machine learning: <\/b><span style=\"font-weight: 400;\">Prediction basing on the information.<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">It becomes clear why it is important to know about conditional probability.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-d6eb003 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d6eb003\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-cf81d63\" data-id=\"cf81d63\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ff6024a elementor-widget elementor-widget-text-editor\" data-id=\"ff6024a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><b>Conditional Probability vs. Normal Probability<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-dba062e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"dba062e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7e083e3\" data-id=\"7e083e3\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c6bd374 elementor-widget elementor-widget-html\" data-id=\"c6bd374\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<section class=\"probability-comparison\" aria-labelledby=\"probability-comparison-title\">\n  <h2 id=\"probability-comparison-title\">\n    Conditional Probability vs. Normal Probability\n  <\/h2>\n\n  <p>\n    Although they are related, <strong>normal probability<\/strong> and\n    <strong>conditional probability<\/strong> are not exactly the same.\n    The main difference is whether we use additional information about an event.\n  <\/p>\n\n  <div class=\"probability-table-wrapper\">\n    <table class=\"probability-table\">\n      <caption>\n        Comparison of normal probability and conditional probability\n      <\/caption>\n\n      <thead>\n        <tr>\n          <th scope=\"col\">Normal Probability<\/th>\n          <th scope=\"col\">Conditional Probability<\/th>\n        <\/tr>\n      <\/thead>\n\n      <tbody>\n        <tr>\n          <td>Finds the chance of an event occurring.<\/td>\n          <td>Finds the chance of an event under a known condition.<\/td>\n        <\/tr>\n\n        <tr>\n          <td>May not require additional information.<\/td>\n          <td>Uses additional information that is already known.<\/td>\n        <\/tr>\n\n        <tr>\n          <td>\n            <strong>Example:<\/strong> Chance of rolling a 6 on a die.\n          <\/td>\n          <td>\n            <strong>Example:<\/strong> Chance of rolling a 6 given that the\n            number rolled is even.\n          <\/td>\n        <\/tr>\n      <\/tbody>\n    <\/table>\n  <\/div>\n\n  <div class=\"probability-key-point\">\n    <strong>Key Difference:<\/strong>\n    Conditional probability considers information or a condition that is\n    already known, while normal probability looks at the likelihood of an\n    event without that additional condition.\n  <\/div>\n<\/section>\n\n<style>\n  .probability-comparison {\n    max-width: 100%;\n    margin: 30px auto;\n    font-family: Arial, sans-serif;\n    color: #222;\n    line-height: 1.7;\n  }\n\n  .probability-comparison h2 {\n    margin-bottom: 12px;\n    font-size: 28px;\n    line-height: 1.3;\n  }\n\n  .probability-comparison p {\n    margin-bottom: 20px;\n    font-size: 16px;\n  }\n\n  .probability-table-wrapper {\n    width: 100%;\n    overflow-x: auto;\n    margin: 20px 0;\n    border-radius: 10px;\n  }\n\n  .probability-table {\n    width: 100%;\n    min-width: 600px;\n    border-collapse: collapse;\n    background: #ffffff;\n    border: 1px solid #ddd;\n  }\n\n  .probability-table caption {\n    text-align: left;\n    font-size: 15px;\n    font-weight: 600;\n    margin-bottom: 10px;\n  }\n\n  .probability-table th {\n    padding: 15px;\n    text-align: left;\n    font-size: 17px;\n    font-weight: 700;\n    border: 1px solid #ddd;\n    background: #f3f6fa;\n  }\n\n  .probability-table td {\n    padding: 15px;\n    vertical-align: top;\n    font-size: 16px;\n    border: 1px solid #ddd;\n  }\n\n  .probability-table tbody tr:nth-child(even) {\n    background: #fafafa;\n  }\n\n  .probability-table tbody tr:hover {\n    background: #f5f8fc;\n  }\n\n  .probability-key-point {\n    margin-top: 20px;\n    padding: 16px 18px;\n    border-left: 4px solid #333;\n    background: #f7f7f7;\n    font-size: 16px;\n  }\n\n  @media (max-width: 600px) {\n    .probability-comparison h2 {\n      font-size: 23px;\n    }\n\n    .probability-comparison p,\n    .probability-table td {\n      font-size: 15px;\n    }\n\n    .probability-table th {\n      font-size: 15px;\n    }\n\n    .probability-table td,\n    .probability-table th {\n      padding: 12px;\n    }\n  }\n<\/style>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-1839773 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1839773\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b570e13\" data-id=\"b570e13\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-806b0b1 elementor-widget elementor-widget-text-editor\" data-id=\"806b0b1\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><b>Conclusion<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-adb3466 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"adb3466\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-03bcc07\" data-id=\"03bcc07\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-aa5ef15 elementor-widget elementor-widget-text-editor\" data-id=\"aa5ef15\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<div class=\"flex max-w-full flex-col gap-4 grow\"><div class=\"min-h-8 text-message relative flex w-full flex-col items-end gap-2 text-start break-words whitespace-normal outline-none keyboard-focused:focus-ring [.text-message+&amp;]:mt-1\" dir=\"auto\" tabindex=\"0\" data-message-author-role=\"assistant\" data-message-id=\"8b3e7343-d013-4c02-9ce3-13b57189159f\" data-message-model-slug=\"gpt-5-6-mini\" data-turn-start-message=\"true\"><div class=\"flex w-full flex-col gap-1 empty:hidden\"><div class=\"markdown prose dark:prose-invert wrap-break-word w-full light markdown-new-styling\"><p><b>Conditional probability<\/b><span style=\"font-weight: 400;\"> helps us calculate the chance of an event when another event is already known to have happened. The main <\/span><b>conditional probability formula<\/b><span style=\"font-weight: 400;\"> is <\/span><b>P(A | B) = P(A \u2229 B) \/ P(B)<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><p><span style=\"font-weight: 400;\">The easiest way to understand conditional probability is to remember one idea: <\/span><b>new information can change the probability of an event<\/b><span style=\"font-weight: 400;\">. By practicing different <\/span><b>conditional probability examples<\/b><span style=\"font-weight: 400;\">, you can become more comfortable identifying the condition, choosing the correct sample space, and applying the formula.<\/span><\/p><p data-start=\"0\" data-end=\"174\" data-is-last-node=\"\" data-is-only-node=\"\">You can opt for our\u00a0<a href=\"https:\/\/moonpreneur.com\/innovator-program\/advanced-math\/\">Advanced Math<\/a>\u00a0or Vedic Math+Mental Math courses. Our\u00a0<a href=\"https:\/\/mp.moonpreneur.com\/math-quiz-for-kids\/\">Math Quiz<\/a>\u00a0for grades 3rd, 4th, 5th, and 6th helps in further exciting and engaging in mathematics with hands-on lessons.<\/p><\/div><\/div><\/div><\/div>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Ever had the question of how the probability of an event will be affected by having prior knowledge about the event? Here comes the application of conditional probability. Conditional probability is used to determine the probability of an event given that another event has taken place. For instance, in trying to determine the probability of [&hellip;]<\/p>\n","protected":false},"author":116,"featured_media":41374,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[969,1035],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/41349"}],"collection":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/users\/116"}],"replies":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/comments?post=41349"}],"version-history":[{"count":23,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/41349\/revisions"}],"predecessor-version":[{"id":41377,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/41349\/revisions\/41377"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/media\/41374"}],"wp:attachment":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/media?parent=41349"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/categories?post=41349"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/tags?post=41349"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}