{"id":58842,"date":"2020-04-16T19:58:33","date_gmt":"2020-04-16T19:58:33","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=58842"},"modified":"2026-03-28T11:16:28","modified_gmt":"2026-03-28T16:16:28","slug":"conditional-probability","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/conditional-probability\/","title":{"rendered":"Conditional Probability"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_akvIihDjXuA\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_akvIihDjXuA\" data-source-videoID=\"akvIihDjXuA\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Conditional Probability Video\" height=\"720\" width=\"1280\" class=\"size-full\" data-matomo-title = \"Conditional Probability\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_akvIihDjXuA:hover {cursor:pointer;} img#videoThumbnailImage_akvIihDjXuA {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Conitional-Probability-thumb.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_akvIihDjXuA\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_akvIihDjXuA\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Conditional Probability\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_akvIihDjXuA\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_akvIihDjXuA\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_akvIihDjXuA\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction P4T_Function() {\n  var x = document.getElementById(\"P4T\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"P4T_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"P4T\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Review_of_Basic_Probability\" class=\"smooth-scroll\">Review of Basic Probability<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Conditional_Probability\" class=\"smooth-scroll\">Conditional Probability<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Conditional_Probability_Practice_Questions\" class=\"smooth-scroll\">Conditional Probability Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Today, we\u2019re going to take a look at <strong>conditional probability<\/strong>. This type of probability is all about finding the odds of something happening given that something else has already occurred.<\/p>\n<h2><span id=\"Review_of_Basic_Probability\" class=\"m-toc-anchor\"><\/span>Review of Basic Probability<\/h2>\n<p>\nLet\u2019s start with a refresher on <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/multiplication-rule-of-probability\/\">basic probability<\/a>. The probability of something happening can be expressed as the number of desired outcomes divided by the number of total possible outcomes: <\/p>\n<div class=\"examplesentence\">\\(P(A)\\)\\(\\text{ }=\\text{ }\\)<span style=\"font-size: 110%;\">\\(\\frac{\\text{Number of desired outcomes}}{\\text{Total number of possible outcomes}}\\)<\/span><\/div>\n<p>\n&nbsp;<\/p>\n<h3><span id=\"Example_1_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nHere\u2019s an example of a basic probability problem. There are 10 marbles in a bag: three are blue, three are red, and four are orange. What are the odds of pulling out a red marble?<\/p>\n<p>To solve this, we\u2019d place the number of desired outcomes on the top (in this case, it&#8217;s 3 because there are three red marbles) and the total number of possible outcomes on the bottom (this is 10 since there are 10 total marbles in the bag). <\/p>\n<div class=\"examplesentence\">\\(P(A)\\)\\(\\text{ }=\\text{ }\\)<span style=\"font-size: 125%;\">\\(\\frac{3\\text{ red marbles}}{10\\text{ total marbles}}\\)<\/span><\/div>\n<p>\n&nbsp;<br \/>\nSeems pretty straightforward, right? <\/p>\n<h2><span id=\"Conditional_Probability\" class=\"m-toc-anchor\"><\/span>Conditional Probability<\/h2>\n<p>\nWell, conditional probability adds a bit of a twist to this, as the objects or people in question often have more than one possible attribute. <\/p>\n<h3><span id=\"Example_1_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nLet\u2019s look at an example problem with more than one possible attribute.<\/p>\n<p>Out of 100 houses sold, 50 had a garage, 40 had a pool, and of these, 10 had both a garage and a pool, leaving 20 houses with neither. Given that a house had a garage, what are the odds that it also had a pool? <\/p>\n<p>What do we do with all this information? If we draw it as a Venn diagram, we can make more sense of it: <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/10\/Houses-sold.svg\" alt=\"\" width=\"628\" height=\"419\" class=\"aligncenter size-full wp-image-229062\"  role=\"img\" \/><\/p>\n<p>We can now see the overlap between the houses sold with garages and the houses sold with pools, all within the larger set of houses sold. It\u2019s easier to see now that of the 50 houses sold with a garage, 10 of them also had a pool. So the odds are \\(\\frac{10}{50}\\), which can be expressed as the <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/converting-fractions-to-percentages-and-decimals\/\">fraction<\/a> \\(\\frac{1}{5}\\), or 20%. <\/p>\n<p>Fortunately, there\u2019s a faster way to do this than by drawing a diagram every time you encounter a conditional probability question. <\/p>\n<h3><span id=\"Conditional_Probability_Formula\" class=\"m-toc-anchor\"><\/span>Conditional Probability Formula<\/h3>\n<p>\nThere\u2019s a handy formula we can use: <\/p>\n<div class=\"examplesentence\">\\(P(B|A)=\\frac{P(B\\text{ and }A)}{P(A)}\\)<\/div>\n<p>\n&nbsp;<br \/>\nWe read this formula as \u201cthe probability P of event B happening given that event A has happened is equal to the probability of events B and A both happening over the probability that event A has happened.\u201d<\/p>\n<p>In these types of problems, both probabilities on the right side of the equation are usually given or can be determined from a sentence or table. So in our sample problem, the \\(P(B|A)\\) is the 10 houses that were sold with both a garage and a swimming pool, out of the total 100 houses. This fraction can be written as \\(\\frac{1}{10}\\). <\/p>\n<p>The P(A) is the probability of a house being sold with a garage (event A), which is 50 houses out of the 100, or \\(\\frac{5}{10}\\). Now that our formula is complete, we can divide \\(\\frac{1}{10}\\) by \\(\\frac{5}{10}\\) and we get \\(\\frac{1}{5}\\), which is equal to 20%, just as we figured out from our diagram. <\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nLet\u2019s try one more with numbers that aren\u2019t quite so neat. <\/p>\n<p>In a small town, there are 216 men: 144 of them have brown hair and 56 of them have mustaches. 24 of the men have brown hair and mustaches. What are the odds that a man chosen at random has a mustache given that he has brown hair? <\/p>\n<p>Let\u2019s plug into our formula. The probability of event A (brown hair) <em>and<\/em> event B (mustache) is the 24 men with both, divided by the 216 total men. <\/p>\n<p>The probability of event A is 144 divided by the 216 total men. We divide \\(\\frac{24}{216}\\) by \\(\\frac{144}{216}\\) using fraction division. The 216s can be canceled out, so we are left with \\(\\frac{24}{144}\\). This fraction can be reduced to \\(\\frac{1}{6}\\), or \u224816.67%.<\/p>\n<p>All right, that&#8217;s all for this review. I hope this increased your odds of understanding conditional probability.<\/p>\n<p>Thanks for watching, and happy studying!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Conditional_Probability_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Conditional Probability Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the formula for conditional probability?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">\\(P(B|A)=\\frac{P(A)}{P(B)}\\)<\/div><div class=\"PQ\"  id=\"PQ-1-2\">\\(P(B|A)=\\frac{P(B)}{P(A)}\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-3\">\\(P(B|A)=\\frac{P(A\\text{ and }B)}{P(A)}\\)<\/div><div class=\"PQ\"  id=\"PQ-1-4\">\\(P(B|A)=\\frac{P(B\\text{ and }A)}{P(A\\text{ and }B)}\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The conditional probability formula allows us to determine the probability that Event <em>B<\/em> will occur, given the knowledge that Event <em>A<\/em> has already occurred. \\(P(B|A)\\) stands for \u201cthe probability of <em>B<\/em> given <em>A<\/em>.\u201d The probability of Event <em>B<\/em> can be determined by dividing the probability of Events <em>A<\/em> and <em>B<\/em> occurring by the probability of Event <em>A<\/em> occurring. <\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nThe Venn diagram below shows sections for the probability of Event <em>A<\/em> occurring and the probability of Event <em>B<\/em> occurring. What does the shaded middle section represent?<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/11\/Venn-diagram-A-and-B.svg\" alt=\"A Venn diagram with two overlapping circles labeled A and B; the intersection area is shaded gray.\" width=\"356.4\" height=\"217.8\" class=\"aligncenter size-full wp-image-275458\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">The shaded middle section represents \\(P(\\frac{A}{B})\\) <\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-2\">The shaded middle section represents \\(P(A\\text{ and }B)\\) <\/div><div class=\"PQ\"  id=\"PQ-2-3\">The shaded middle section represents \\(P(A\\text{ not occurring})\\) <\/div><div class=\"PQ\"  id=\"PQ-2-4\">The shaded middle section represents \\(P(B\\text{ not occurring})\\) <\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The middle section of the Venn diagram represents the overlap of Events <em>A<\/em> and <em>B<\/em>, where both events occur. <\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhich Venn diagram represents the following scenario: <\/p>\n<p>100 customers have purchased cars at Jason\u2019s car dealership this year. 40 of those customers purchased cars with touch-screen GPS, and 30 customers purchased cars with snow tires. 20 customers purchased cars with both touch-screen GPS and snow tires. <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-3-1\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Venn-Diagram-Example-A.svg\" alt=\"Venn diagram showing 40 have only touch-screen GPS, 30 have only snow tires, and 20 have both features.\" width=\"295\" height=\"193\" class=\"alignnone size-full wp-image-287690\"  role=\"img\" \/><\/div><div class=\"PQ\"  id=\"PQ-3-2\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Venn-Diagram-Example-B.svg\" alt=\"Venn diagram showing 50 have only touch-screen GPS, 30 have only snow tires, and 10 have both.\" width=\"295\" height=\"193\" class=\"alignnone size-full wp-image-287693\"  role=\"img\" \/><\/div><div class=\"PQ\"  id=\"PQ-3-3\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Venn-Diagram-Example-C.svg\" alt=\"Venn diagram displaying 40 with touch-screen GPS only, 20 with snow tires only, and 50 with both features.\" width=\"295\" height=\"193\" class=\"alignnone  size-full wp-image-287696\"  role=\"img\" \/><\/div><div class=\"PQ\"  id=\"PQ-3-4\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Venn-Diagram-Example-D.svg\" alt=\"Venn diagram showing 35 have touch-screen GPS only, 25 have snow tires only, and 50 have both touch-screen GPS and snow tires.\" width=\"295\" height=\"193\" class=\"alignnone size-full wp-image-287699\"  role=\"img\" \/><\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The far left portion of the Venn diagram represents the customers who purchased cars with touch-screen GPS but no snow tires. The far right portion of the Venn diagram represents the customers who purchased cars with snow tires but not touch-screen GPS. The middle section represents customers who purchased cars with both touch-screen GPS and snow tires.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nConsider the same group of 100 customers from Jason\u2019s car dealership. 40 purchased GPS, 30 purchased snow tires, and 20 purchased both. If a randomly selected customer has purchased the GPS, what would the probability be that they also purchased the snow tires? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">20%<\/div><div class=\"PQ\"  id=\"PQ-4-2\">30%<\/div><div class=\"PQ\"  id=\"PQ-4-3\">40%<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-4\">50%<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The conditional probability formula can be used to solve this problem. The probability of Event A occurring (customer purchasing GPS) is 40 out of 100 customers, or 0.4. The probability of Event <em>B<\/em> occurring (customer purchasing snow tires) is 30 out of 100, or 0.3. The probability of a customer purchasing both, or Event <em>A<\/em> and <em>B<\/em> occurring, is 20 out of 100, or 0.2.<\/p>\n<p>We know P(A) = 0.4 and P (<em>A<\/em> and <em>B<\/em>) = 0.2 so we can plug these into the formula. <\/p>\n<p>\\(P(A)=\\frac{P(A \\text{ and } B)}{P(A)}\\) becomes \\(P(B|A)=\\frac{0.2}{0.4}\\), which simplifies to 0.5, or 50%. <\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nSybil took two science tests. The probability of her passing both tests is 0.6 and the probability of her passing the first test is 0.8. What is the probability of her passing the second test if she passed the first test? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">65% chance of passing the second test <\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-2\">75% chance of passing the second test <\/div><div class=\"PQ\"  id=\"PQ-5-3\">85% chance of passing the second test <\/div><div class=\"PQ\"  id=\"PQ-5-4\">95% chance of passing the second test <\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The conditional probability formula can be used to solve this problem. The probability of Event <em>A<\/em> occurring (passing the first test) is 0.8. The probability of Event <em>A<\/em> and <em>B<\/em> occurring (passing both tests) is 0.6. <\/p>\n<p>We know \\(P(A)=0.8\\) and \\(P(A\\text{ and }B)=0.6\\) so we can plug these into the formula. <\/p>\n<p>\\(P(B|A)=\\frac{P(A\\text{ and }B)}{P(A)}\\) becomes \\(P(B|A)=\\frac{0.6}{0.8}\\) which simplifies to 0.75 or 75%.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/probability\/\">Return to Probability Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Probability Videos<\/p>\n","protected":false},"author":1,"featured_media":229056,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-58842","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-math-advertising-group","7":"page_category-probability-videos","8":"page_type-video","9":"content_type-practice-questions","10":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/58842","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=58842"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/58842\/revisions"}],"predecessor-version":[{"id":229059,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/58842\/revisions\/229059"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/229056"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=58842"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}