{"id":4962,"date":"2022-08-17T16:09:51","date_gmt":"2022-08-17T16:09:51","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=4962"},"modified":"2022-08-17T16:20:44","modified_gmt":"2022-08-17T16:20:44","slug":"7b-preview","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/7b-preview\/","title":{"raw":"7B Preview","rendered":"7B Preview"},"content":{"raw":"Preparing for the next class\r\n\r\nIn the next in-class activity, you will need to understand how to calculate theoretical\u00a0 probabilities involving the words AND, OR, and NOT.\r\n
\r\n

Question 1<\/h3>\r\nIn May 2021, SurveyUSA [footnote]SurveyUSA. (2021, May 3). Results of SurveyUSA News Poll #25925<\/em>. https:\/\/www.surveyusa.com\/client\/PollReport.aspx?g=e3ae1d7e-9d6e-44b2-b1f8-e51c51df9ea2[\/footnote] interviewed 750 California adults and asked a number of\u00a0 questions related to voting. One of the questions asked was:\r\n\r\n\u201cAre you registered to vote in California?\u201d\r\n\r\nSurveyUSA reported the following survey results.\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Are you registered to\u00a0 vote in California?<\/td>\r\nYes<\/td>\r\n645<\/td>\r\n<\/tr>\r\n
No<\/td>\r\n98<\/td>\r\n<\/tr>\r\n
Not Sure<\/td>\r\n7<\/td>\r\n<\/tr>\r\n
Total<\/td>\r\n750<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n
    \r\n \t
  1. What is the probability that a randomly selected California adult is registered\u00a0 to vote? Round to the nearest hundredth.<\/li>\r\n \t
  2. What is the probability that a randomly selected California adult is not\u00a0 registered to vote? Round to the nearest hundredth.<\/li>\r\n \t
  3. What is the probability that a randomly selected California adult is not sure if\u00a0 they are registered to vote? Round to the nearest thousandth.<\/li>\r\n \t
  4. Rounding to the nearest whole number, what is the sum of the probabilities you computed in Parts A through C?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n
    \r\n

    Question 2<\/h3>\r\nThe same survey also asked the 750 respondents to identify their age group from \u00a0one of the following groups:\r\n\r\n18-34, 35-49, 50-64, 65+\r\n
      \r\n \t
    1. The following are the frequencies for each age group. Fill in the missing \u00a0value in the table.\r\nWhat age group do you belong to?\r\n
      \r\n\r\n\r\n\r\n\r\n
      18\u201334<\/td>\r\n35\u201349<\/td>\r\n50\u201364<\/td>\r\n65+<\/td>\r\nTotal<\/td>\r\n<\/tr>\r\n
      233<\/td>\r\n195<\/td>\r\n180<\/td>\r\n<\/td>\r\n750<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div><\/li>\r\n \t
    2. What is the probability that a randomly selected California adult is 65 years \u00a0old or older? Round to the nearest hundredth.<\/li>\r\n \t
    3. What is the probability that a randomly selected California adult is less than \u00a065 years old? Round to the nearest hundredth.<\/li>\r\n \t
    4. What is the relationship between the probabilities calculated in Parts B and \u00a0C? \u00a0Hint: Think about their sum.<\/li>\r\n<\/ol>\r\n<\/div>\r\nThe event that a California adult is less than 65 years old can be written as the event \u00a0\u201cNOT 65+.\u201d\r\n\r\nThese two events, 65+ and NOT 65+, are referred to as complements because the \u00a0sum of their probabilities is equal to 1.\r\n\r\nMore generally, for any event A, we can think of the probability of complements as \u00a0having the following relationship:\r\n\r\n[latex] P(A) + P(NOT A) = 1 [\/latex]\r\n\r\nThe equation can be rewritten as follows:\r\n\r\n[latex] P(NOT A) = 1 - P(A) [\/latex]\r\n\r\nThis tells us that for event A, the probability that the event will not occur is equal to 1 \u00a0minus the probability that the event will occur.\r\n
      \r\n

      Question 3<\/h3>\r\nWhat is the complement of the event \u201c18\u201334?\u201d\r\n\r\nHint: Use the plus symbol like it is used in 65+.\r\n\r\n<\/div>\r\n
      \r\n

      Question 4<\/h3>\r\nSuppose we want to investigate the answers to both questions in the survey in the \u00a0same table as follows:\r\n\r\nWhat age group do you belong to?\r\n
      \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
      <\/td>\r\n<\/td>\r\n18\u201334<\/td>\r\n35\u201349<\/td>\r\n50\u201364<\/td>\r\n65+<\/td>\r\nTotal<\/td>\r\n<\/tr>\r\n
      Are you registered\u00a0 to vote in\r\n\r\nCalifornia?<\/td>\r\nYes<\/td>\r\n180<\/td>\r\n175<\/td>\r\n151<\/td>\r\n139<\/td>\r\n645<\/td>\r\n<\/tr>\r\n
      No<\/td>\r\n49<\/td>\r\n20<\/td>\r\n27<\/td>\r\n3<\/td>\r\n98<\/td>\r\n<\/tr>\r\n
      Not Sure<\/td>\r\n4<\/td>\r\n0<\/td>\r\n2<\/td>\r\n0<\/td>\r\n7<\/td>\r\n<\/tr>\r\n
      Total<\/td>\r\n233<\/td>\r\n195<\/td>\r\n180<\/td>\r\n142<\/td>\r\n750<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
        \r\n \t
      1. What is the probability that a randomly selected adult from California is \u00a0registered to vote? Notice where you found the counts used in your \u00a0calculations on the table. Round to the nearest hundredth.<\/li>\r\n \t
      2. What is the probability that a randomly selected adult from California is 65+? \u00a0Notice where you found the counts used in your calculations on the table. \u00a0Round to the nearest hundredth.\r\n\r\nThere are times when you want to combine two events with using the word AND or\u00a0 the word OR.\r\n\r\nAs an example, you may want to find the probability of it raining OR snowing on a\u00a0 given day so that you can dress accordingly.\r\n\r\nIn probability, AND means that both events must happen, and OR means one event,\u00a0 the other event, or both events must happen.<\/li>\r\n \t
      3. What is the probability that a randomly selected adult from California is 65+ \u00a0AND registered to vote? Round to the nearest hundredth.\r\n\r\nWhen it is impossible for two events to happen at the same time, they are called\u00a0 mutually-exclusive events. If A and B are mutually-exclusive events, then:\r\n\r\n[latex] P(A AND B) = 0 [\/latex]\r\n\r\nand\r\n\r\n[latex] P(A or B) = P(A) + P(B) [\/latex]<\/li>\r\n \t
      4. \u00a0What is the probability that a randomly selected adult from California is 18\u2013 34 AND 35\u201349? Round to the nearest hundredth.\r\n\r\nHint: Is it possible to be in two age groups?<\/li>\r\n \t
      5. What is the probability that a randomly selected adult from California is 18\u2013 34 OR 35\u201349? Round to the nearest hundredth.\r\n\r\nHint: Are \u201c18\u201334\u201d and \u201c35\u201349\u201d mutually-exclusive events? If so, use the formula.<\/li>\r\n<\/ol>\r\n<\/div>\r\n \r\n\r\n \r\n\r\n ","rendered":"

        Preparing for the next class<\/p>\n

        In the next in-class activity, you will need to understand how to calculate theoretical\u00a0 probabilities involving the words AND, OR, and NOT.<\/p>\n

        \n

        Question 1<\/h3>\n

        In May 2021, SurveyUSA [1]<\/sup><\/a> interviewed 750 California adults and asked a number of\u00a0 questions related to voting. One of the questions asked was:<\/p>\n

        \u201cAre you registered to vote in California?\u201d<\/p>\n

        SurveyUSA reported the following survey results.<\/p>\n

        \n\n\n\n\n\n\n
        Are you registered to\u00a0 vote in California?<\/td>\nYes<\/td>\n645<\/td>\n<\/tr>\n
        No<\/td>\n98<\/td>\n<\/tr>\n
        Not Sure<\/td>\n7<\/td>\n<\/tr>\n
        Total<\/td>\n750<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
          \n
        1. What is the probability that a randomly selected California adult is registered\u00a0 to vote? Round to the nearest hundredth.<\/li>\n
        2. What is the probability that a randomly selected California adult is not\u00a0 registered to vote? Round to the nearest hundredth.<\/li>\n
        3. What is the probability that a randomly selected California adult is not sure if\u00a0 they are registered to vote? Round to the nearest thousandth.<\/li>\n
        4. Rounding to the nearest whole number, what is the sum of the probabilities you computed in Parts A through C?<\/li>\n<\/ol>\n<\/div>\n<\/div>\n
          \n

          Question 2<\/h3>\n

          The same survey also asked the 750 respondents to identify their age group from \u00a0one of the following groups:<\/p>\n

          18-34, 35-49, 50-64, 65+<\/p>\n

            \n
          1. The following are the frequencies for each age group. Fill in the missing \u00a0value in the table.
            \nWhat age group do you belong to?<\/p>\n
            \n\n\n\n\n
            18\u201334<\/td>\n35\u201349<\/td>\n50\u201364<\/td>\n65+<\/td>\nTotal<\/td>\n<\/tr>\n
            233<\/td>\n195<\/td>\n180<\/td>\n<\/td>\n750<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/li>\n
          2. What is the probability that a randomly selected California adult is 65 years \u00a0old or older? Round to the nearest hundredth.<\/li>\n
          3. What is the probability that a randomly selected California adult is less than \u00a065 years old? Round to the nearest hundredth.<\/li>\n
          4. What is the relationship between the probabilities calculated in Parts B and \u00a0C? \u00a0Hint: Think about their sum.<\/li>\n<\/ol>\n<\/div>\n

            The event that a California adult is less than 65 years old can be written as the event \u00a0\u201cNOT 65+.\u201d<\/p>\n

            These two events, 65+ and NOT 65+, are referred to as complements because the \u00a0sum of their probabilities is equal to 1.<\/p>\n

            More generally, for any event A, we can think of the probability of complements as \u00a0having the following relationship:<\/p>\n

            [latex]P(A) + P(NOT A) = 1[\/latex]<\/p>\n

            The equation can be rewritten as follows:<\/p>\n

            [latex]P(NOT A) = 1 - P(A)[\/latex]<\/p>\n

            This tells us that for event A, the probability that the event will not occur is equal to 1 \u00a0minus the probability that the event will occur.<\/p>\n

            \n

            Question 3<\/h3>\n

            What is the complement of the event \u201c18\u201334?\u201d<\/p>\n

            Hint: Use the plus symbol like it is used in 65+.<\/p>\n<\/div>\n

            \n

            Question 4<\/h3>\n

            Suppose we want to investigate the answers to both questions in the survey in the \u00a0same table as follows:<\/p>\n

            What age group do you belong to?<\/p>\n

            \n\n\n\n\n\n\n\n
            <\/td>\n<\/td>\n18\u201334<\/td>\n35\u201349<\/td>\n50\u201364<\/td>\n65+<\/td>\nTotal<\/td>\n<\/tr>\n
            Are you registered\u00a0 to vote in<\/p>\n

            California?<\/td>\n

            		Yes<\/td>\n180<\/td>\n175<\/td>\n151<\/td>\n139<\/td>\n645<\/td>\n<\/tr>\n
            No<\/td>\n49<\/td>\n20<\/td>\n27<\/td>\n3<\/td>\n98<\/td>\n<\/tr>\n
            Not Sure<\/td>\n4<\/td>\n0<\/td>\n2<\/td>\n0<\/td>\n7<\/td>\n<\/tr>\n
            Total<\/td>\n233<\/td>\n195<\/td>\n180<\/td>\n142<\/td>\n750<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
              \n
            1. What is the probability that a randomly selected adult from California is \u00a0registered to vote? Notice where you found the counts used in your \u00a0calculations on the table. Round to the nearest hundredth.<\/li>\n
            2. What is the probability that a randomly selected adult from California is 65+? \u00a0Notice where you found the counts used in your calculations on the table. \u00a0Round to the nearest hundredth.\n

              There are times when you want to combine two events with using the word AND or\u00a0 the word OR.<\/p>\n

              As an example, you may want to find the probability of it raining OR snowing on a\u00a0 given day so that you can dress accordingly.<\/p>\n

              In probability, AND means that both events must happen, and OR means one event,\u00a0 the other event, or both events must happen.<\/li>\n

            3. What is the probability that a randomly selected adult from California is 65+ \u00a0AND registered to vote? Round to the nearest hundredth.\n

              When it is impossible for two events to happen at the same time, they are called\u00a0 mutually-exclusive events. If A and B are mutually-exclusive events, then:<\/p>\n

              [latex]P(A AND B) = 0[\/latex]<\/p>\n

              and<\/p>\n

              [latex]P(A or B) = P(A) + P(B)[\/latex]<\/li>\n

            4. \u00a0What is the probability that a randomly selected adult from California is 18\u2013 34 AND 35\u201349? Round to the nearest hundredth.\n

              Hint: Is it possible to be in two age groups?<\/li>\n

            5. What is the probability that a randomly selected adult from California is 18\u2013 34 OR 35\u201349? Round to the nearest hundredth.\n

              Hint: Are \u201c18\u201334\u201d and \u201c35\u201349\u201d mutually-exclusive events? If so, use the formula.<\/li>\n<\/ol>\n<\/div>\n

               <\/p>\n

               <\/p>\n

               <\/p>\n

              1. SurveyUSA. (2021, May 3). Results of SurveyUSA News Poll #25925<\/em>. https:\/\/www.surveyusa.com\/client\/PollReport.aspx?g=e3ae1d7e-9d6e-44b2-b1f8-e51c51df9ea2 ↵<\/a><\/li><\/ol><\/div>","protected":false},"author":574340,"menu_order":7,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4962","chapter","type-chapter","status-publish","hentry"],"part":4871,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4962","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/574340"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4962\/revisions"}],"predecessor-version":[{"id":4964,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4962\/revisions\/4964"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/4871"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4962\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=4962"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=4962"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=4962"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=4962"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}