{"id":5000,"date":"2022-08-17T17:37:54","date_gmt":"2022-08-17T17:37:54","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=5000"},"modified":"2022-08-17T17:39:57","modified_gmt":"2022-08-17T17:39:57","slug":"8a-coreq","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/8a-coreq\/","title":{"raw":"8A Coreq","rendered":"8A Coreq"},"content":{"raw":"In the next preview assignment and in the next class, you will need to think critically\u00a0 about the number of \u201csuccesses\u201d that would occur if a chance experiment were\u00a0 repeated multiple times.\r\n\r\nHow Many \u201cSuccesses\u201d Do We Expect?\r\n\r\nAt a college baseball stadium, every game features a race between three mascots: one\u00a0 dressed as a peanut, one dressed as a hot dog, and one dressed as a cup of soda. The\u00a0 winner of the race determines what discount will be available at the concession stand\u00a0 for the rest of the game: $1 bags of peanuts, $1 hot dogs, or $1 soft drinks. For now,\u00a0 let\u2019s assume that all three mascots are equally likely to win the race, and each race is\u00a0 independent.\r\n
\r\n

Question 1<\/h3>\r\nFill in the following table with the probability of each mascot winning the race.\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Outcome<\/td>\r\nProbability<\/td>\r\n<\/tr>\r\n
Peanut<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Hot Dog<\/td>\r\n<\/td>\r\n<\/tr>\r\n
Soda<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\nLet\u2019s say you plan to attend two games. Let\u2019s list all possible outcomes for the two races. \u201cPeanut \u2013 Peanut\u201d means the peanut wins in both the first race and the second\u00a0 race, \u201cPeanut \u2013 Hot Dog\u201d means the peanut wins in the first race and the hot dog wins\u00a0 in the second race, and so on.\r\n
\r\n\r\n\r\n\r\n\r\n\r\n
Peanut \u2013 Peanut<\/td>\r\nHot Dog \u2013 Peanut<\/td>\r\nSoda \u2013 Peanut<\/td>\r\n<\/tr>\r\n
Peanut \u2013 Hot Dog<\/td>\r\nHot Dog \u2013 Hot Dog<\/td>\r\nSoda \u2013 Hot Dog<\/td>\r\n<\/tr>\r\n
Peanut \u2013 Soda<\/td>\r\nHot Dog \u2013 Soda<\/td>\r\nSoda \u2013 Soda<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n
\r\n

Question 2<\/h3>\r\nMaybe your favorite snack to eat during a baseball game is peanuts.\r\n
    \r\n \t
  1. For each of the nine outcomes, record the number of times the peanut wins\u00a0 by writing the number in the previous table.<\/li>\r\n \t
  2. Assuming all three mascots are equally likely to win in each race, what is the\u00a0 probability that the peanut will win 0 times out of the two baseball games you\u00a0 attend? Write your answer as a fraction.<\/li>\r\n \t
  3. Assuming all three mascots are equally likely to win in each race, what is the\u00a0 probability that the peanut will win 1 time out of the two baseball games you\u00a0 attend? Write your answer as a fraction.<\/li>\r\n \t
  4. Assuming all three mascots are equally likely to win in each race, what is the\u00a0 probability that the peanut will win 2 times out of the two baseball games you\u00a0 attend? Write your answer as a fraction.<\/li>\r\n \t
  5. Fill in the following table to show the probability of each number of peanut\u00a0 wins.\r\n
    \r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Number\u00a0 of Wins\r\n\r\n(Peanut)<\/td>\r\nProbability<\/td>\r\n<\/tr>\r\n
    <\/td>\r\n<\/td>\r\n<\/tr>\r\n
    <\/td>\r\n<\/td>\r\n<\/tr>\r\n
    <\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div><\/li>\r\n \t
  6. Compare the table in Question 1 to the table in Question 2, Part E. How are\u00a0 they different?<\/li>\r\n<\/ol>\r\n<\/div>\r\nThe previous probability calculations were based on a list of all possible outcomes. This\u00a0 is a reasonable approach for two races because the list of outcomes is fairly short, but it\u00a0 wouldn\u2019t work well for a larger set of races. For 10 races, there would be over 50,000\u00a0 possible outcomes!\r\n\r\nAnother approach would be to estimate the probabilities empirically using a simulation.\u00a0 Since we\u2019re assuming all three mascots are equally likely to win in each race, a\u00a0 statistics class decides to carry out the simulation by rolling dice: 1 and 2 represent\u00a0 Peanut, 3 and 4 represent Hot Dog, and 5 and 6 represent Soda.\r\n\r\nHow many times would you expect to get discounted peanuts if you attended 10\u00a0 games? The following plot shows one possible set of 10 races, based on a student\u2019s\u00a0 simulation using dice.\r\n\r\n\"\"\r\n
    \r\n

    Question 3<\/h3>\r\nWhat does each dot in the plot represent?\r\n
      \r\n \t
    1. The winner of one race<\/li>\r\n \t
    2. The number of times the peanut won in a set of 10 races<\/li>\r\n<\/ol>\r\n<\/div>\r\n
      \r\n

      Question 4<\/h3>\r\nIn this simulated set of 10 races, how many times did the peanut win?\r\n\r\n<\/div>\r\n
      \r\n

      Question 5<\/h3>\r\nIf another student used the same approach to simulate 10 races using dice, would\u00a0 they get the same results?\r\n\r\n<\/div>\r\nSuppose there are 24 students in a statistics class. Each student simulated a set of 10 races by rolling a fair die 10 times and recording how many times the peanut won.\r\n\r\n\"\"\r\n
      \r\n

      Question 6<\/h3>\r\nWhat does each dot in the plot represent?\r\n
        \r\n \t
      1. The winner of one race<\/li>\r\n \t
      2. The number of times the peanut won in a set of 10 races<\/li>\r\n<\/ol>\r\n<\/div>\r\n
        \r\n

        Question 7<\/h3>\r\nBased on the previous dotplot, estimate the following probabilities. Give your answer\u00a0 as a simplified fraction and a decimal rounded to the nearest thousandth.\r\n
          \r\n \t
        1. Estimate the probability that the peanut will win exactly 3 times out of 10.<\/li>\r\n \t
        2. Estimate the probability that the peanut will win 6 or more times out of 10.<\/li>\r\n \t
        3. Estimate the probability that the peanut will win 2 or fewer times out of 10.<\/li>\r\n \t
        4. Compare the probabilities in Parts B and C. Which of these events is less\u00a0 likely? How can you tell by looking at the simplified fractions?<\/li>\r\n \t
        5. Compare the probabilities in Parts B and C. How can you tell which value is\u00a0 smaller by looking the decimals?<\/li>\r\n<\/ol>\r\n<\/div>\r\n \r\n\r\n ","rendered":"

          In the next preview assignment and in the next class, you will need to think critically\u00a0 about the number of \u201csuccesses\u201d that would occur if a chance experiment were\u00a0 repeated multiple times.<\/p>\n

          How Many \u201cSuccesses\u201d Do We Expect?<\/p>\n

          At a college baseball stadium, every game features a race between three mascots: one\u00a0 dressed as a peanut, one dressed as a hot dog, and one dressed as a cup of soda. The\u00a0 winner of the race determines what discount will be available at the concession stand\u00a0 for the rest of the game: $1 bags of peanuts, $1 hot dogs, or $1 soft drinks. For now,\u00a0 let\u2019s assume that all three mascots are equally likely to win the race, and each race is\u00a0 independent.<\/p>\n

          \n

          Question 1<\/h3>\n

          Fill in the following table with the probability of each mascot winning the race.<\/p>\n

          \n\n\n\n\n\n\n
          Outcome<\/td>\nProbability<\/td>\n<\/tr>\n
          Peanut<\/td>\n<\/td>\n<\/tr>\n
          Hot Dog<\/td>\n<\/td>\n<\/tr>\n
          Soda<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

          Let\u2019s say you plan to attend two games. Let\u2019s list all possible outcomes for the two races. \u201cPeanut \u2013 Peanut\u201d means the peanut wins in both the first race and the second\u00a0 race, \u201cPeanut \u2013 Hot Dog\u201d means the peanut wins in the first race and the hot dog wins\u00a0 in the second race, and so on.<\/p>\n

          \n\n\n\n\n\n
          Peanut \u2013 Peanut<\/td>\nHot Dog \u2013 Peanut<\/td>\nSoda \u2013 Peanut<\/td>\n<\/tr>\n
          Peanut \u2013 Hot Dog<\/td>\nHot Dog \u2013 Hot Dog<\/td>\nSoda \u2013 Hot Dog<\/td>\n<\/tr>\n
          Peanut \u2013 Soda<\/td>\nHot Dog \u2013 Soda<\/td>\nSoda \u2013 Soda<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n
          \n

          Question 2<\/h3>\n

          Maybe your favorite snack to eat during a baseball game is peanuts.<\/p>\n

            \n
          1. For each of the nine outcomes, record the number of times the peanut wins\u00a0 by writing the number in the previous table.<\/li>\n
          2. Assuming all three mascots are equally likely to win in each race, what is the\u00a0 probability that the peanut will win 0 times out of the two baseball games you\u00a0 attend? Write your answer as a fraction.<\/li>\n
          3. Assuming all three mascots are equally likely to win in each race, what is the\u00a0 probability that the peanut will win 1 time out of the two baseball games you\u00a0 attend? Write your answer as a fraction.<\/li>\n
          4. Assuming all three mascots are equally likely to win in each race, what is the\u00a0 probability that the peanut will win 2 times out of the two baseball games you\u00a0 attend? Write your answer as a fraction.<\/li>\n
          5. Fill in the following table to show the probability of each number of peanut\u00a0 wins.\n
            \n\n\n\n\n\n\n
            Number\u00a0 of Wins<\/p>\n

            (Peanut)<\/td>\n

            		Probability<\/td>\n<\/tr>\n
            <\/td>\n<\/td>\n<\/tr>\n
            <\/td>\n<\/td>\n<\/tr>\n
            <\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/li>\n
          6. Compare the table in Question 1 to the table in Question 2, Part E. How are\u00a0 they different?<\/li>\n<\/ol>\n<\/div>\n

            The previous probability calculations were based on a list of all possible outcomes. This\u00a0 is a reasonable approach for two races because the list of outcomes is fairly short, but it\u00a0 wouldn\u2019t work well for a larger set of races. For 10 races, there would be over 50,000\u00a0 possible outcomes!<\/p>\n

            Another approach would be to estimate the probabilities empirically using a simulation.\u00a0 Since we\u2019re assuming all three mascots are equally likely to win in each race, a\u00a0 statistics class decides to carry out the simulation by rolling dice: 1 and 2 represent\u00a0 Peanut, 3 and 4 represent Hot Dog, and 5 and 6 represent Soda.<\/p>\n

            How many times would you expect to get discounted peanuts if you attended 10\u00a0 games? The following plot shows one possible set of 10 races, based on a student\u2019s\u00a0 simulation using dice.<\/p>\n

            \"\"<\/p>\n

            \n

            Question 3<\/h3>\n

            What does each dot in the plot represent?<\/p>\n

              \n
            1. The winner of one race<\/li>\n
            2. The number of times the peanut won in a set of 10 races<\/li>\n<\/ol>\n<\/div>\n
              \n

              Question 4<\/h3>\n

              In this simulated set of 10 races, how many times did the peanut win?<\/p>\n<\/div>\n

              \n

              Question 5<\/h3>\n

              If another student used the same approach to simulate 10 races using dice, would\u00a0 they get the same results?<\/p>\n<\/div>\n

              Suppose there are 24 students in a statistics class. Each student simulated a set of 10 races by rolling a fair die 10 times and recording how many times the peanut won.<\/p>\n

              \"\"<\/p>\n

              \n

              Question 6<\/h3>\n

              What does each dot in the plot represent?<\/p>\n

                \n
              1. The winner of one race<\/li>\n
              2. The number of times the peanut won in a set of 10 races<\/li>\n<\/ol>\n<\/div>\n
                \n

                Question 7<\/h3>\n

                Based on the previous dotplot, estimate the following probabilities. Give your answer\u00a0 as a simplified fraction and a decimal rounded to the nearest thousandth.<\/p>\n

                  \n
                1. Estimate the probability that the peanut will win exactly 3 times out of 10.<\/li>\n
                2. Estimate the probability that the peanut will win 6 or more times out of 10.<\/li>\n
                3. Estimate the probability that the peanut will win 2 or fewer times out of 10.<\/li>\n
                4. Compare the probabilities in Parts B and C. Which of these events is less\u00a0 likely? How can you tell by looking at the simplified fractions?<\/li>\n
                5. Compare the probabilities in Parts B and C. How can you tell which value is\u00a0 smaller by looking the decimals?<\/li>\n<\/ol>\n<\/div>\n

                   <\/p>\n

                   <\/p>\n","protected":false},"author":574340,"menu_order":1,"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-5000","chapter","type-chapter","status-publish","hentry"],"part":4997,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5000","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\/5000\/revisions"}],"predecessor-version":[{"id":5005,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5000\/revisions\/5005"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/4997"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/5000\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=5000"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=5000"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=5000"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=5000"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}