{"id":1478,"date":"2013-12-24T09:00:08","date_gmt":"2013-12-24T09:00:08","guid":{"rendered":"https:\/\/magoosh.com\/sat\/?p=1478"},"modified":"2015-04-15T20:09:50","modified_gmt":"2015-04-15T20:09:50","slug":"sat-math-probability","status":"publish","type":"post","link":"https:\/\/magoosh.com\/act\/sat-math-probability\/","title":{"rendered":"SAT Math – Probability"},"content":{"rendered":"

Probability is actually pretty rare on the SAT. So don\u2019t freak out about this topic. In fact, I\u2019d only recommend this post for those looking for a near perfect\u2014those who want to make sure they have all their bases covered.<\/p>\n

What you\u2019ll have to know is the following:<\/p>\n

Probability (Likelihood of something happening) = #of desired outcomes\/# of possible outcomes<\/p>\n

Let\u2019s say we want to know what is the probability of rolling \u201csnake eyes\u201d, or two \u20181\u2019\u2019s, on a pair of fair dice. Well, how many ways can you roll two \u20181\u2019s? There is only one way. So for a desired outcome\u2014the quantity in the numerator\u2014we are going to write \u20181\u2019.<\/p>\n

Now how many different ways can you roll two six-sided dice? (For a review of the Fundamental Counting Principle click here). Well, there are six possibilities on each die, so that gives us 6 x 6 = 36.<\/p>\n

Therefore, the probability of rolling \u201csnake eyes\u201d with two dice is 1\/36.<\/p>\n

Of course things do get a little more complicated with probability\u2014that\u2019s why so many people dread it. Below are some medium- to medium-difficult questions for you to sink your teeth into. If you nail all three, the probability of you struggling with a probability question on the test is very low.<\/p>\n

If not, make sure you understand the concepts (see explanations below), and you should do just fine on the probability questions the SAT throws at you.<\/p>\n

1. A basket contains a total of 24 balls of yarn. 1\/3 are white, \u00bc are red, 1\/6 are blue, and the rest are black. What is the probability, if you reach into the basket, of pulling out either a red or black yarn?<\/p>\n

    \n
  1. \u00bc<\/li>\n
  2. 1\/3<\/li>\n
  3. \u00bd<\/li>\n
  4. 7\/12<\/li>\n
  5. 5\/6<\/li>\n<\/ol>\n

    2. A six-sided die is thrown three times. What is the probability that on all three rolls a prime number will never come up?<\/p>\n

      \n
    1. \u00bd<\/li>\n
    2. 1\/6<\/li>\n
    3. 1\/8<\/li>\n
    4. 1\/64<\/li>\n
    5. 3\/216<\/li>\n<\/ol>\n

      3. A coin is tossed three times. What is the probability that three \u201ctails\u201d in a row will not show up?<\/p>\n

        \n
      1. 1\/8<\/li>\n
      2. 3\/16<\/li>\n
      3. \u00bd<\/li>\n
      4. 5\/8<\/li>\n
      5. 7\/8<\/li>\n<\/ol>\n

         <\/p>\n

        Explanations:<\/h2>\n

        1. Hey, a little fun with fractions never hurt! So, if we do the math, we get 8 white, 6 red, and 4 blue. That means the remaining 6 are black. Since the question asks for red AND black, that gives us 12 (desired outcomes) out of 24 (total outcomes), or \u00bd.<\/p>\n

        2. First off, there are three prime numbers on a six-sided die: 2, 3, and 5. What is the probability of NOT rolling one of these three numbers? 1\/2, since rolling a 1, 4, or 6 would count. Now, the probability of rolling an outcome of \u00bd (or 50%) is much like tossing a coin. In this case, we are tossing the coin, or rolling a die with a \u20181\u2019, \u20184\u2019 or \u20186\u2019, three times: \u00bd x \u00bd x \u00bd = 1\/8. Answer: (C).<\/p>\n

        3. Speaking of coins! A quick way of doing this problem is subtracting the probability of getting all tails by the total probability. Before we do that a quick thing on the probability space. Usually, we talk about something definitely happening as having a probability of 100%. However, 1 also represents a 100%. How? Well, if the probability of something happening is \u00bd or 50%, what happens when you multiply both those numbers by 2? You get \u20181\u2019 and 100%. So probability can be defined along a scale from \u20180\u2019 to \u20181\u2019.<\/p>\n

        So for the coin toss, \u20181\u2019 represents all possible outcomes. Subtracting the probability of all tails from \u20181\u2019 will give us the probability of NOT getting on tails: 1 \u2013 (1\/2)^3 = 1 \u2013 1\/8 = 7\/8. (E).<\/p>\n

         <\/p>\n","protected":false},"excerpt":{"rendered":"

        Probability is actually pretty rare on the SAT. So don\u2019t freak out about this topic. In fact, I\u2019d only recommend this post for those looking for a near perfect\u2014those who want to make sure they have all their bases covered. What you\u2019ll have to know is the following: Probability (Likelihood of something happening) = #of […]<\/p>\n","protected":false},"author":10,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[90],"tags":[9,122,60],"ppma_author":[24882],"class_list":["post-1478","post","type-post","status-publish","format-standard","hentry","category-all","tag-act-math","tag-act-probability","tag-sat-statistics"],"acf":[],"yoast_head":"\nSAT Probability<\/title>\n<meta name=\"description\" content=\"Probability is actually pretty rare on the SAT. So don\u2019t freak out about this topic.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/magoosh.com\/act\/sat-math-probability\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"SAT Math - Probability\" \/>\n<meta property=\"og:description\" content=\"Probability is actually pretty rare on the SAT. So don\u2019t freak out about this topic.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/magoosh.com\/act\/sat-math-probability\/\" \/>\n<meta property=\"og:site_name\" content=\"Magoosh Blog | ACT\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/MagooshSat\/\" \/>\n<meta property=\"article:author\" content=\"https:\/\/www.facebook.com\/ChrisLeleMagoosh1\/\" \/>\n<meta property=\"article:published_time\" content=\"2013-12-24T09:00:08+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2015-04-15T20:09:50+00:00\" \/>\n<meta name=\"author\" content=\"Chris Lele\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@chrismagoosh\" \/>\n<meta name=\"twitter:site\" content=\"@MagooshSAT_ACT\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Chris Lele\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/magoosh.com\/act\/sat-math-probability\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/act\/sat-math-probability\/\"},\"author\":{\"name\":\"Chris Lele\",\"@id\":\"https:\/\/magoosh.com\/act\/#\/schema\/person\/3b6630b4f786513b81a860849cffd546\"},\"headline\":\"SAT Math – Probability\",\"datePublished\":\"2013-12-24T09:00:08+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/magoosh.com\/act\/sat-math-probability\/\"},\"wordCount\":547,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/act\/#organization\"},\"keywords\":[\"ACT Math Test\",\"ACT Probability\",\"SAT Statistics\"],\"articleSection\":[\"ACT\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/magoosh.com\/act\/sat-math-probability\/\",\"url\":\"https:\/\/magoosh.com\/act\/sat-math-probability\/\",\"name\":\"SAT Probability\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/act\/#website\"},\"datePublished\":\"2013-12-24T09:00:08+00:00\",\"description\":\"Probability is actually pretty rare on the SAT. So don\u2019t freak out about this topic.\",\"breadcrumb\":{\"@id\":\"https:\/\/magoosh.com\/act\/sat-math-probability\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/magoosh.com\/act\/sat-math-probability\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/magoosh.com\/act\/sat-math-probability\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/magoosh.com\/act\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"SAT Math – Probability\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/magoosh.com\/act\/#website\",\"url\":\"https:\/\/magoosh.com\/act\/\",\"name\":\"Magoosh Blog | ACT\",\"description\":\"ACT Information and Practice\",\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/act\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/magoosh.com\/act\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/magoosh.com\/act\/#organization\",\"name\":\"Magoosh\",\"url\":\"https:\/\/magoosh.com\/act\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/magoosh.com\/act\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/magoosh.com\/act\/files\/2019\/02\/Magoosh-logo-purple-60h.png\",\"contentUrl\":\"https:\/\/magoosh.com\/act\/files\/2019\/02\/Magoosh-logo-purple-60h.png\",\"width\":265,\"height\":60,\"caption\":\"Magoosh\"},\"image\":{\"@id\":\"https:\/\/magoosh.com\/act\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/MagooshSat\/\",\"https:\/\/twitter.com\/MagooshSAT_ACT\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/magoosh.com\/act\/#\/schema\/person\/3b6630b4f786513b81a860849cffd546\",\"name\":\"Chris Lele\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/magoosh.com\/act\/#\/schema\/person\/image\/0acb1b2097fd77b56ab6475c9b41cb27\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/39381a6b4ab74cd4c87c7e678683c33c3b18f1e14f6f0ac762a946185968952b?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/39381a6b4ab74cd4c87c7e678683c33c3b18f1e14f6f0ac762a946185968952b?s=96&d=mm&r=g\",\"caption\":\"Chris Lele\"},\"description\":\"Chris graduated from UCLA with a BA in Psychology and has 20 years of experience in the test prep industry. He's been quoted as a subject expert in many publications, including US News, GMAC, and Business Because.\",\"sameAs\":[\"https:\/\/www.facebook.com\/ChrisLeleMagoosh1\/\",\"ttps:\/\/www.linkedin.com\/in\/chris-lele-095005a0\",\"https:\/\/twitter.com\/chrismagoosh\",\"https:\/\/www.youtube.com\/channel\/UCZ4sGYJ6l0cgnVNIHY8GY6w\"],\"knowsAbout\":[\"GRE\",\"GMAT\",\"SAT\",\"ACT\",\"MCAT (CARS)\",\"LSAT\"],\"jobTitle\":\"Principal Curriculum Manager\",\"worksFor\":\"Magoosh\",\"url\":\"https:\/\/magoosh.com\/act\/author\/chris\/\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"SAT Probability","description":"Probability is actually pretty rare on the SAT. So don\u2019t freak out about this topic.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/magoosh.com\/act\/sat-math-probability\/","og_locale":"en_US","og_type":"article","og_title":"SAT Math - Probability","og_description":"Probability is actually pretty rare on the SAT. So don\u2019t freak out about this topic.","og_url":"https:\/\/magoosh.com\/act\/sat-math-probability\/","og_site_name":"Magoosh Blog | ACT","article_publisher":"https:\/\/www.facebook.com\/MagooshSat\/","article_author":"https:\/\/www.facebook.com\/ChrisLeleMagoosh1\/","article_published_time":"2013-12-24T09:00:08+00:00","article_modified_time":"2015-04-15T20:09:50+00:00","author":"Chris Lele","twitter_card":"summary_large_image","twitter_creator":"@chrismagoosh","twitter_site":"@MagooshSAT_ACT","twitter_misc":{"Written by":"Chris Lele","Est. reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/magoosh.com\/act\/sat-math-probability\/#article","isPartOf":{"@id":"https:\/\/magoosh.com\/act\/sat-math-probability\/"},"author":{"name":"Chris Lele","@id":"https:\/\/magoosh.com\/act\/#\/schema\/person\/3b6630b4f786513b81a860849cffd546"},"headline":"SAT Math – Probability","datePublished":"2013-12-24T09:00:08+00:00","mainEntityOfPage":{"@id":"https:\/\/magoosh.com\/act\/sat-math-probability\/"},"wordCount":547,"commentCount":0,"publisher":{"@id":"https:\/\/magoosh.com\/act\/#organization"},"keywords":["ACT Math Test","ACT Probability","SAT Statistics"],"articleSection":["ACT"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/magoosh.com\/act\/sat-math-probability\/","url":"https:\/\/magoosh.com\/act\/sat-math-probability\/","name":"SAT Probability","isPartOf":{"@id":"https:\/\/magoosh.com\/act\/#website"},"datePublished":"2013-12-24T09:00:08+00:00","description":"Probability is actually pretty rare on the SAT. So don\u2019t freak out about this topic.","breadcrumb":{"@id":"https:\/\/magoosh.com\/act\/sat-math-probability\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/magoosh.com\/act\/sat-math-probability\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/magoosh.com\/act\/sat-math-probability\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/magoosh.com\/act\/"},{"@type":"ListItem","position":2,"name":"SAT Math – Probability"}]},{"@type":"WebSite","@id":"https:\/\/magoosh.com\/act\/#website","url":"https:\/\/magoosh.com\/act\/","name":"Magoosh Blog | ACT","description":"ACT Information and Practice","publisher":{"@id":"https:\/\/magoosh.com\/act\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/magoosh.com\/act\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/magoosh.com\/act\/#organization","name":"Magoosh","url":"https:\/\/magoosh.com\/act\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/magoosh.com\/act\/#\/schema\/logo\/image\/","url":"https:\/\/magoosh.com\/act\/files\/2019\/02\/Magoosh-logo-purple-60h.png","contentUrl":"https:\/\/magoosh.com\/act\/files\/2019\/02\/Magoosh-logo-purple-60h.png","width":265,"height":60,"caption":"Magoosh"},"image":{"@id":"https:\/\/magoosh.com\/act\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/MagooshSat\/","https:\/\/twitter.com\/MagooshSAT_ACT"]},{"@type":"Person","@id":"https:\/\/magoosh.com\/act\/#\/schema\/person\/3b6630b4f786513b81a860849cffd546","name":"Chris Lele","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/magoosh.com\/act\/#\/schema\/person\/image\/0acb1b2097fd77b56ab6475c9b41cb27","url":"https:\/\/secure.gravatar.com\/avatar\/39381a6b4ab74cd4c87c7e678683c33c3b18f1e14f6f0ac762a946185968952b?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/39381a6b4ab74cd4c87c7e678683c33c3b18f1e14f6f0ac762a946185968952b?s=96&d=mm&r=g","caption":"Chris Lele"},"description":"Chris graduated from UCLA with a BA in Psychology and has 20 years of experience in the test prep industry. He's been quoted as a subject expert in many publications, including US News, GMAC, and Business Because.","sameAs":["https:\/\/www.facebook.com\/ChrisLeleMagoosh1\/","ttps:\/\/www.linkedin.com\/in\/chris-lele-095005a0","https:\/\/twitter.com\/chrismagoosh","https:\/\/www.youtube.com\/channel\/UCZ4sGYJ6l0cgnVNIHY8GY6w"],"knowsAbout":["GRE","GMAT","SAT","ACT","MCAT (CARS)","LSAT"],"jobTitle":"Principal Curriculum Manager","worksFor":"Magoosh","url":"https:\/\/magoosh.com\/act\/author\/chris\/"}]}},"authors":[{"term_id":24882,"user_id":10,"is_guest":0,"slug":"chris","display_name":"Chris Lele","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/39381a6b4ab74cd4c87c7e678683c33c3b18f1e14f6f0ac762a946185968952b?s=96&d=mm&r=g","user_url":"","last_name":"Lele","first_name":"Chris","description":"Chris Lele is the Principal Curriculum Manager (and <a href=\"https:\/\/www.amazon.com\/Vocabulary-Builder-Workbook-Activities-Must-Know\/dp\/193975481X\" rel=\"noopener noreferrer\">vocabulary wizard<\/a>) at Magoosh. Chris graduated from UCLA with a BA in Psychology and has 20 years of experience in the test prep industry. He's been quoted as a subject expert in many publications, including<a href=\"https:\/\/www.usnews.com\/education\/best-colleges\/slideshows\/10-test-prep-tips-for-sat-and-act-takers\" rel=\"noopener noreferrer\"> US News<\/a>,<a href=\"https:\/\/www.mba.com\/exams-and-exam-prep\/gmat-exam\/why-take-the-gmat-in-2021-when-many-schools-are-test-optional\" rel=\"noopener noreferrer\"> GMAC<\/a>, and<a href=\"https:\/\/www.businessbecause.com\/news\/gmat\/3263\/mba-admissions-gre-challenges-gmat\" rel=\"noopener noreferrer\"> Business Because<\/a>.\r\n\r\n\r\nIn his time at Magoosh, Chris has taught countless students how to tackle the<a href=\"https:\/\/www.amazon.com\/GRE-Prep-Magoosh\/dp\/1939418917\/\" rel=\"noopener noreferrer\"> GRE<\/a>, GMAT, SAT, ACT, MCAT (CARS), and LSAT exams with confidence. Some of his students have even gone on to get near-perfect scores. You can find Chris on <a href=\"https:\/\/www.youtube.com\/channel\/UCZ4sGYJ6l0cgnVNIHY8GY6w\">YouTube<\/a>,<a href=\"https:\/\/www.linkedin.com\/in\/chris-lele-095005a0\"> LinkedIn<\/a>, <a href=\"https:\/\/twitter.com\/chrismagoosh\">Twitter<\/a> and <a href=\"https:\/\/www.facebook.com\/ChrisLeleMagoosh1\/\">Facebook<\/a>!"}],"_links":{"self":[{"href":"https:\/\/magoosh.com\/act\/wp-json\/wp\/v2\/posts\/1478","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/magoosh.com\/act\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/magoosh.com\/act\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/magoosh.com\/act\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/magoosh.com\/act\/wp-json\/wp\/v2\/comments?post=1478"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/act\/wp-json\/wp\/v2\/posts\/1478\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/act\/wp-json\/wp\/v2\/media?parent=1478"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/act\/wp-json\/wp\/v2\/categories?post=1478"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/act\/wp-json\/wp\/v2\/tags?post=1478"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/act\/wp-json\/wp\/v2\/ppma_author?post=1478"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}