{"id":4974,"date":"2022-08-17T16:59:59","date_gmt":"2022-08-17T16:59:59","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=4974"},"modified":"2022-08-17T17:01:12","modified_gmt":"2022-08-17T17:01:12","slug":"7c-preview","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/7c-preview\/","title":{"raw":"7C Preview","rendered":"7C Preview"},"content":{"raw":"Preparing for the next class\r\n\r\nIn the next in-class activity, you will need to calculate conditional probabilities,\u00a0 probabilities relating to independent events, and probabilities relating to mutually exclusive events.\r\n\r\nIn previous discussions of probability, we might have given you information on Rafael\u2019s\u00a0 activities and then asked, \u201cWhat is the probability that Rafael rides his bike?\u201d\r\n\r\nIn this activity, we will calculate probabilities in the presence of additional information. For example, \u201cGiven that it is raining, what is the probability that Rafael rides his bike?\u201d\r\n\r\nLet\u2019s try.\r\n
\r\n

Question 1<\/h3>\r\nDiamond has four phone cases. Two phone cases have a pop socket while the other\u00a0 two do not. Every morning, Diamond closes her eyes and randomly selects one\u00a0 phone case to use for the day.\r\n
    \r\n \t
  1. What is the probability that Diamond selects a phone case with a pop\u00a0 socket?<\/li>\r\n \t
  2. One morning, before Diamond wakes up, her little sister borrows one of the\u00a0 cases with a pop socket. Given that Diamond\u2019s sister has taken one of the\u00a0 pop socket phone cases, what is the probability that Diamond randomly\u00a0 selects a phone case with a pop socket?\r\nHint: There is one phone case with a pop socket in the three remaining phone\u00a0 cases.We call the probability in Part B a conditional probability because we calculated\u00a0 Diamond\u2019s probability of selecting a case with a pop socket conditional on the fact\u00a0 that her sister had taken one of her cases. We write this as:\r\nP(Diamond selects case with pop socket GIVEN her sister took one case with pop socket)\r\nThe probability of Diamond selecting a phone case with a pop socket is impacted by\u00a0 her sister borrowing one of the phone cases. In this example, one event occurring impacts the probability of another event occurring. However, this is not always the\u00a0 case.\r\n\r\nSometimes, there are pairs of events for which one event has no effect on the\u00a0 probability of another event occurring. When this is the case, we say the events are\u00a0 independent. More formally:\r\nEvents A and B are independent if [latex] P(A~GIVEN~B) = P(A) [\/latex]<\/li>\r\n \t
  3. Determine whether the following is true or false:P(Diamond selects case with pop socket GIVEN her sister took one case\u00a0 with pop socket) = P(Diamond selects case with pop socket)\r\n\r\nHint: Are your answers to Parts A and B the same?<\/li>\r\n \t
  4. Determine whether the following statement is true or false:Whether Diamond selects a phone case with a pop socket is independent of\u00a0 her sister borrowing one of her pop socket phone cases.<\/li>\r\n<\/ol>\r\n<\/div>\r\n
    \r\n

    Question 2<\/h3>\r\nOn any given day, the probability of Rafael checking his email is 0.9. The weather\u00a0 does not affect the probability of him checking his email.\r\n
      \r\n \t
    1. Do you think rainy weather and Rafael checking his email are independent\u00a0 events?\r\nHint: The problem tells us the weather does not affect the probability of him checking\u00a0 his email.<\/li>\r\n \t
    2. Calculate the probability of Rafael checking his email conditional on the fact\u00a0 that it is raining. That is, calculate: P(Rafael checks his email GIVEN\u00a0 Raining).\r\nHint: The probability of checking email on a rainy day is the same as the probability\u00a0 of checking email in general.<\/li>\r\n<\/ol>\r\n<\/div>\r\n
      \r\n

      Question 3<\/h3>\r\nFor each part, determine whether the two events are independent.\r\n
        \r\n \t
      1. Rafael avoids riding his bike in the rain. Is biking to work independent of\u00a0 rain?\r\nHint: If the rain affects Rafael\u2019s probability of biking, then the two events are not\u00a0 independent.<\/li>\r\n \t
      2. On any given day, the probability that Hiroki wears sneakers is 85%. On\u00a0 Fridays, the probability that Hiroki wears sneakers is 85%. Is wearing\u00a0 sneakers independent of whether it\u2019s a Friday?<\/li>\r\n<\/ol>\r\n<\/div>\r\nRecall that two events are mutually exclusive if the probability of both events happening\u00a0 at the same time is zero. For example, consider flipping a coin. It can land heads up or\u00a0 heads down, but it cannot be both heads up and heads down simultaneously. Thus,\u00a0 heads and tails are mutually-exclusive events.\r\n
        \r\n

        Question 4<\/h3>\r\nFor each part, determine if the pair of events are mutually exclusive.\r\n
          \r\n \t
        1. The weather is rainy and Rafael checks his email\r\nHint: Is P(Rafael checks his email and it\u2019s raining) = 0?<\/li>\r\n \t
        2. Eating a steak and being veganHint: A person is vegan if they do not eat meat.<\/li>\r\n \t
        3. Wearing shoes and being barefoot<\/li>\r\n \t
        4. Wearing a dress and having pockets<\/li>\r\n<\/ol>\r\n<\/div>\r\n ","rendered":"

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

          In the next in-class activity, you will need to calculate conditional probabilities,\u00a0 probabilities relating to independent events, and probabilities relating to mutually exclusive events.<\/p>\n

          In previous discussions of probability, we might have given you information on Rafael\u2019s\u00a0 activities and then asked, \u201cWhat is the probability that Rafael rides his bike?\u201d<\/p>\n

          In this activity, we will calculate probabilities in the presence of additional information. For example, \u201cGiven that it is raining, what is the probability that Rafael rides his bike?\u201d<\/p>\n

          Let\u2019s try.<\/p>\n

          \n

          Question 1<\/h3>\n

          Diamond has four phone cases. Two phone cases have a pop socket while the other\u00a0 two do not. Every morning, Diamond closes her eyes and randomly selects one\u00a0 phone case to use for the day.<\/p>\n

            \n
          1. What is the probability that Diamond selects a phone case with a pop\u00a0 socket?<\/li>\n
          2. One morning, before Diamond wakes up, her little sister borrows one of the\u00a0 cases with a pop socket. Given that Diamond\u2019s sister has taken one of the\u00a0 pop socket phone cases, what is the probability that Diamond randomly\u00a0 selects a phone case with a pop socket?
            \nHint: There is one phone case with a pop socket in the three remaining phone\u00a0 cases.We call the probability in Part B a conditional probability because we calculated\u00a0 Diamond\u2019s probability of selecting a case with a pop socket conditional on the fact\u00a0 that her sister had taken one of her cases. We write this as:
            \nP(Diamond selects case with pop socket GIVEN her sister took one case with pop socket)
            \nThe probability of Diamond selecting a phone case with a pop socket is impacted by\u00a0 her sister borrowing one of the phone cases. In this example, one event occurring impacts the probability of another event occurring. However, this is not always the\u00a0 case.<\/p>\n

            Sometimes, there are pairs of events for which one event has no effect on the\u00a0 probability of another event occurring. When this is the case, we say the events are\u00a0 independent. More formally:
            \nEvents A and B are independent if [latex]P(A~GIVEN~B) = P(A)[\/latex]<\/li>\n

          3. Determine whether the following is true or false:P(Diamond selects case with pop socket GIVEN her sister took one case\u00a0 with pop socket) = P(Diamond selects case with pop socket)\n

            Hint: Are your answers to Parts A and B the same?<\/li>\n

          4. Determine whether the following statement is true or false:Whether Diamond selects a phone case with a pop socket is independent of\u00a0 her sister borrowing one of her pop socket phone cases.<\/li>\n<\/ol>\n<\/div>\n
            \n

            Question 2<\/h3>\n

            On any given day, the probability of Rafael checking his email is 0.9. The weather\u00a0 does not affect the probability of him checking his email.<\/p>\n

              \n
            1. Do you think rainy weather and Rafael checking his email are independent\u00a0 events?
              \nHint: The problem tells us the weather does not affect the probability of him checking\u00a0 his email.<\/li>\n
            2. Calculate the probability of Rafael checking his email conditional on the fact\u00a0 that it is raining. That is, calculate: P(Rafael checks his email GIVEN\u00a0 Raining).
              \nHint: The probability of checking email on a rainy day is the same as the probability\u00a0 of checking email in general.<\/li>\n<\/ol>\n<\/div>\n
              \n

              Question 3<\/h3>\n

              For each part, determine whether the two events are independent.<\/p>\n

                \n
              1. Rafael avoids riding his bike in the rain. Is biking to work independent of\u00a0 rain?
                \nHint: If the rain affects Rafael\u2019s probability of biking, then the two events are not\u00a0 independent.<\/li>\n
              2. On any given day, the probability that Hiroki wears sneakers is 85%. On\u00a0 Fridays, the probability that Hiroki wears sneakers is 85%. Is wearing\u00a0 sneakers independent of whether it\u2019s a Friday?<\/li>\n<\/ol>\n<\/div>\n

                Recall that two events are mutually exclusive if the probability of both events happening\u00a0 at the same time is zero. For example, consider flipping a coin. It can land heads up or\u00a0 heads down, but it cannot be both heads up and heads down simultaneously. Thus,\u00a0 heads and tails are mutually-exclusive events.<\/p>\n

                \n

                Question 4<\/h3>\n

                For each part, determine if the pair of events are mutually exclusive.<\/p>\n

                  \n
                1. The weather is rainy and Rafael checks his email
                  \nHint: Is P(Rafael checks his email and it\u2019s raining) = 0?<\/li>\n
                2. Eating a steak and being veganHint: A person is vegan if they do not eat meat.<\/li>\n
                3. Wearing shoes and being barefoot<\/li>\n
                4. Wearing a dress and having pockets<\/li>\n<\/ol>\n<\/div>\n

                   <\/p>\n","protected":false},"author":574340,"menu_order":10,"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-4974","chapter","type-chapter","status-publish","hentry"],"part":4871,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4974","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\/4974\/revisions"}],"predecessor-version":[{"id":4982,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4974\/revisions\/4982"}],"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\/4974\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=4974"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=4974"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=4974"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=4974"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}