{"id":1478,"date":"2013-12-24t09:00:08","date_gmt":"2013-12-24t09:00:08","guid":{"rendered":"\/\/www.catharsisit.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":"\/\/www.catharsisit.com\/hs\/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],"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=\"\/\/www.catharsisit.com\/hs\/act\/sat-math-probability\/\" \/>\n<meta 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lele","image":{"@type":"imageobject","inlanguage":"en-us","@id":"\/\/www.catharsisit.com\/hs\/#\/schema\/person\/image\/9f063fdc4c0268d1eac74c41e0906a03","url":"https:\/\/secure.gravatar.com\/avatar\/198545d5a4baea0ba0fd0c0fc8a5d466?s=96&d=mm&r=g","contenturl":"https:\/\/secure.gravatar.com\/avatar\/198545d5a4baea0ba0fd0c0fc8a5d466?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":"\/\/www.catharsisit.com\/hs\/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\/198545d5a4baea0ba0fd0c0fc8a5d466?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":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/posts\/1478"}],"collection":[{"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/comments?post=1478"}],"version-history":[{"count":0,"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/posts\/1478\/revisions"}],"wp:attachment":[{"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/media?parent=1478"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/categories?post=1478"},{"taxonomy":"post_tag","embeddable":true,"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/tags?post=1478"},{"taxonomy":"author","embeddable":true,"href":"\/\/www.catharsisit.com\/hs\/wp-json\/wp\/v2\/ppma_author?post=1478"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}