{"id":224,"date":"2023-01-17T17:57:12","date_gmt":"2023-01-17T22:57:12","guid":{"rendered":"https:\/\/opentextbc.ca\/busstatsancillary\/?post_type=chapter&#038;p=224"},"modified":"2023-01-20T13:50:55","modified_gmt":"2023-01-20T18:50:55","slug":"two-basic-rules-of-probability","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/busstatsancillary\/chapter\/two-basic-rules-of-probability\/","title":{"raw":"3.3 Two Basic Rules of Probability","rendered":"3.3 Two Basic Rules of Probability"},"content":{"raw":"The following activities and questions relate to material covered in <a href=\"https:\/\/openstax.org\/books\/introductory-business-statistics\/pages\/3-3-two-basic-rules-of-probability\">Chapter 3.3 Two Basic Rules of Probability<\/a>\u00a0in\u00a0<a href=\"https:\/\/openstax.org\/details\/books\/introductory-business-statistics\" target=\"_blank\" rel=\"noopener\"><em>Introductory Business Statistics (OpenStax)<\/em><\/a>.\r\n<div class=\"textbox\">Data sets for the following questions are available in Excel: <a href=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/426\/2023\/01\/3.3-Data-Sets.xlsx\">3.3 Data Sets [XLSX]<\/a>.<\/div>\r\n<h1>Questions<\/h1>\r\n<ol>\r\n \t<li>According to the Yukon Bureau of Statistics, the total population of the Yukon territory in the year 2016 was 35,874 people. [footnote]Data source: Yukon Bureau of Statistics. (2016). <em>Yukon Census historical population, 1901 to 2016<\/em>. https:\/\/yukon.ca\/sites\/yukon.ca\/files\/ybs\/fin-yukon-census-historical-population-1901-2016.pdf.\u00a0[\/footnote]\r\n<ul>\r\n \t<li>From the 2016 census we see that 32,538 people spoke English most often at home.<\/li>\r\n \t<li>3,336 people reported speaking a language other than English most often at home.<\/li>\r\n \t<li>Of those who speak another language at home, 0.2% spoke an aboriginal language most often at home.<\/li>\r\n<\/ul>\r\nLet:\r\n<ul>\r\n \t<li>E = speaks English most often, at home.<\/li>\r\n \t<li>E\u2019= Speaks another language most often, at home.<\/li>\r\n \t<li>A = Speaks an aboriginal language most often, at home.<\/li>\r\n<\/ul>\r\nFinish each probability statement. Check your work after answering b. by making sure P(E) + P(E\u2019) = 1.\r\n<ol type=\"a\">\r\n \t<li>P(E\u2019)<\/li>\r\n \t<li>P(E)<\/li>\r\n \t<li>P(A \u2229 E\u2032)<\/li>\r\n \t<li>P(A | E\u2032)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Yukon University is looking to ask the local caf\u00e9 to cater some desserts for a faculty meeting. The caf\u00e9 makes cookies with chocolate (36%) and nuts (12%) and, of those, 8% contain both chocolate and nuts. Let\u2019s imagine an instructor attending the meeting is allergic to both chocolate and nuts but wants a safe cookie to eat from this selection.\r\n<ol type=\"a\">\r\n \t<li>Find the probability that a cookie contains chocolate or nuts (they cannot eat the cookies).<\/li>\r\n \t<li>Find the probability that a cookie does not contain chocolate or nuts (they can eat the cookie)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>The table below is the roster from newly renamed Edmonton Elks (formerly \u201cEskimos\u201d).\r\n<table class=\"grid\" style=\"width: 100%;\"><caption>Weight of Edmonton Elks Roster [footnote]Data source: Edmonton Elks. (n.d.). <em>Roster<\/em>. https:\/\/www.goelks.com\/roster\/[\/footnote]<\/caption>\r\n<tbody>\r\n<tr>\r\n<th scope=\"col\">Jersey Number (J) \/ Weight (W)<\/th>\r\n<th scope=\"col\">\u2264200 lbs<\/th>\r\n<th scope=\"col\">201 \u2013 231 lbs<\/th>\r\n<th scope=\"col\">232 \u2013 262 lbs<\/th>\r\n<th scope=\"col\">\u2265263 lbs<\/th>\r\n<\/tr>\r\n<tr>\r\n<td>1 - 33<\/td>\r\n<td>9<\/td>\r\n<td>6<\/td>\r\n<td>2<\/td>\r\n<td>0<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>34 - 66<\/td>\r\n<td>4<\/td>\r\n<td>3<\/td>\r\n<td>4<\/td>\r\n<td>7<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>67 - 99<\/td>\r\n<td>9<\/td>\r\n<td>1<\/td>\r\n<td>1<\/td>\r\n<td>4<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nFor the following, suppose that you randomly selected one player from the Elks roster.\r\n<ol type=\"a\">\r\n \t<li>Find the probability that the jersey number is from 1 - 33.<\/li>\r\n \t<li>Find the probability that the player weighs at most 200 pounds.<\/li>\r\n \t<li>Find the probability that their jersey number is from 1 - 33 AND the player weighs at most 200 pounds.<\/li>\r\n \t<li>Find the probability that their jersey number is from 1 - 33 OR the player weighs at most 200 pounds.<\/li>\r\n \t<li>Find the probability that their jersey number is from 1 - 33 GIVEN that the player weighs at most 200 pounds.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n<h1>Solutions<\/h1>\r\n<ol>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>P(E\u2019) = [latex]\\dfrac{3,336}{35,874}[\/latex] = 0.093 or 9.3%<\/li>\r\n \t<li>P(E) = [latex]\\dfrac{32,538}{35,874}[\/latex] = 0.907 or 90.7%.\r\n<strong><em>Check your work by making sure P(E) + P(E\u2019) = 1!<\/em><\/strong><\/li>\r\n \t<li>P(A \u2229 E\u2032) = [latex]\\dfrac{7}{35,874}[\/latex] = 0.0002 or 0.02%<\/li>\r\n \t<li>P (A | E\u2032) = P(A \u2229 E\u2032) \/ P(E\u2019) = [latex]\\dfrac{0.0002}{0.093}[\/latex] = 0.0022<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Let:\r\nC = the event that the cookie contains chocolate.\r\nN = the event that the cookie contains nuts.\r\n<ol type=\"a\">\r\n \t<li>P(C \u222a N) = P(C) + P(N) \u2013 P(C \u2229 N) = 0.36 + 0.12 \u2013 0.08 = 0.40<\/li>\r\n \t<li>P(NEITHER chocolate NOR nuts) = 1 \u2013 P(C \u222a N) = 1 \u2013 0.40 = 0.60<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>\r\n<ol type=\"a\">\r\n \t<li>P(J = 1-33) = [latex]\\dfrac{17}{50}[\/latex] = 34%<\/li>\r\n \t<li>P(W \u2264 200) = [latex]\\dfrac{22}{50}[\/latex] = 44%<\/li>\r\n \t<li>P(J = 1-33 \u2229 W \u2264 200) = [latex]\\dfrac{9}{50}[\/latex] = 18%<\/li>\r\n \t<li>P(J = 1-33 \u222a W \u2264 200) = [latex]\\dfrac{17}{50} + \\dfrac{22}{50}- \\dfrac{9}{50} = \\dfrac{30}{50}[\/latex] = 60%<\/li>\r\n \t<li>P(J = 1-33 | W \u2264 200) = [latex]\\dfrac{\\text{P}(\\text{J}-33\\cap\\text{W}\\leq200)}{\\text{P}(\\text{W}\\leq200)}=\\dfrac{0.18}{0.44}[\/latex] = 40.9%<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>","rendered":"<p>The following activities and questions relate to material covered in <a href=\"https:\/\/openstax.org\/books\/introductory-business-statistics\/pages\/3-3-two-basic-rules-of-probability\">Chapter 3.3 Two Basic Rules of Probability<\/a>\u00a0in\u00a0<a href=\"https:\/\/openstax.org\/details\/books\/introductory-business-statistics\" target=\"_blank\" rel=\"noopener\"><em>Introductory Business Statistics (OpenStax)<\/em><\/a>.<\/p>\n<div class=\"textbox\">Data sets for the following questions are available in Excel: <a href=\"https:\/\/opentextbc.ca\/busstatsancillary\/wp-content\/uploads\/sites\/426\/2023\/01\/3.3-Data-Sets.xlsx\">3.3 Data Sets [XLSX]<\/a>.<\/div>\n<h1>Questions<\/h1>\n<ol>\n<li>According to the Yukon Bureau of Statistics, the total population of the Yukon territory in the year 2016 was 35,874 people. <a class=\"footnote\" title=\"Data source: Yukon Bureau of Statistics. (2016). Yukon Census historical population, 1901 to 2016. https:\/\/yukon.ca\/sites\/yukon.ca\/files\/ybs\/fin-yukon-census-historical-population-1901-2016.pdf.\u00a0\" id=\"return-footnote-224-1\" href=\"#footnote-224-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a>\n<ul>\n<li>From the 2016 census we see that 32,538 people spoke English most often at home.<\/li>\n<li>3,336 people reported speaking a language other than English most often at home.<\/li>\n<li>Of those who speak another language at home, 0.2% spoke an aboriginal language most often at home.<\/li>\n<\/ul>\n<p>Let:<\/p>\n<ul>\n<li>E = speaks English most often, at home.<\/li>\n<li>E\u2019= Speaks another language most often, at home.<\/li>\n<li>A = Speaks an aboriginal language most often, at home.<\/li>\n<\/ul>\n<p>Finish each probability statement. Check your work after answering b. by making sure P(E) + P(E\u2019) = 1.<\/p>\n<ol type=\"a\">\n<li>P(E\u2019)<\/li>\n<li>P(E)<\/li>\n<li>P(A \u2229 E\u2032)<\/li>\n<li>P(A | E\u2032)<\/li>\n<\/ol>\n<\/li>\n<li>Yukon University is looking to ask the local caf\u00e9 to cater some desserts for a faculty meeting. The caf\u00e9 makes cookies with chocolate (36%) and nuts (12%) and, of those, 8% contain both chocolate and nuts. Let\u2019s imagine an instructor attending the meeting is allergic to both chocolate and nuts but wants a safe cookie to eat from this selection.\n<ol type=\"a\">\n<li>Find the probability that a cookie contains chocolate or nuts (they cannot eat the cookies).<\/li>\n<li>Find the probability that a cookie does not contain chocolate or nuts (they can eat the cookie)<\/li>\n<\/ol>\n<\/li>\n<li>The table below is the roster from newly renamed Edmonton Elks (formerly \u201cEskimos\u201d).<br \/>\n<table class=\"grid\" style=\"width: 100%;\">\n<caption>Weight of Edmonton Elks Roster <a class=\"footnote\" title=\"Data source: Edmonton Elks. (n.d.). Roster. https:\/\/www.goelks.com\/roster\/\" id=\"return-footnote-224-2\" href=\"#footnote-224-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><\/caption>\n<tbody>\n<tr>\n<th scope=\"col\">Jersey Number (J) \/ Weight (W)<\/th>\n<th scope=\"col\">\u2264200 lbs<\/th>\n<th scope=\"col\">201 \u2013 231 lbs<\/th>\n<th scope=\"col\">232 \u2013 262 lbs<\/th>\n<th scope=\"col\">\u2265263 lbs<\/th>\n<\/tr>\n<tr>\n<td>1 &#8211; 33<\/td>\n<td>9<\/td>\n<td>6<\/td>\n<td>2<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>34 &#8211; 66<\/td>\n<td>4<\/td>\n<td>3<\/td>\n<td>4<\/td>\n<td>7<\/td>\n<\/tr>\n<tr>\n<td>67 &#8211; 99<\/td>\n<td>9<\/td>\n<td>1<\/td>\n<td>1<\/td>\n<td>4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>For the following, suppose that you randomly selected one player from the Elks roster.<\/p>\n<ol type=\"a\">\n<li>Find the probability that the jersey number is from 1 &#8211; 33.<\/li>\n<li>Find the probability that the player weighs at most 200 pounds.<\/li>\n<li>Find the probability that their jersey number is from 1 &#8211; 33 AND the player weighs at most 200 pounds.<\/li>\n<li>Find the probability that their jersey number is from 1 &#8211; 33 OR the player weighs at most 200 pounds.<\/li>\n<li>Find the probability that their jersey number is from 1 &#8211; 33 GIVEN that the player weighs at most 200 pounds.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<h1>Solutions<\/h1>\n<ol>\n<li>\n<ol type=\"a\">\n<li>P(E\u2019) = [latex]\\dfrac{3,336}{35,874}[\/latex] = 0.093 or 9.3%<\/li>\n<li>P(E) = [latex]\\dfrac{32,538}{35,874}[\/latex] = 0.907 or 90.7%.<br \/>\n<strong><em>Check your work by making sure P(E) + P(E\u2019) = 1!<\/em><\/strong><\/li>\n<li>P(A \u2229 E\u2032) = [latex]\\dfrac{7}{35,874}[\/latex] = 0.0002 or 0.02%<\/li>\n<li>P (A | E\u2032) = P(A \u2229 E\u2032) \/ P(E\u2019) = [latex]\\dfrac{0.0002}{0.093}[\/latex] = 0.0022<\/li>\n<\/ol>\n<\/li>\n<li>Let:<br \/>\nC = the event that the cookie contains chocolate.<br \/>\nN = the event that the cookie contains nuts.<\/p>\n<ol type=\"a\">\n<li>P(C \u222a N) = P(C) + P(N) \u2013 P(C \u2229 N) = 0.36 + 0.12 \u2013 0.08 = 0.40<\/li>\n<li>P(NEITHER chocolate NOR nuts) = 1 \u2013 P(C \u222a N) = 1 \u2013 0.40 = 0.60<\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"a\">\n<li>P(J = 1-33) = [latex]\\dfrac{17}{50}[\/latex] = 34%<\/li>\n<li>P(W \u2264 200) = [latex]\\dfrac{22}{50}[\/latex] = 44%<\/li>\n<li>P(J = 1-33 \u2229 W \u2264 200) = [latex]\\dfrac{9}{50}[\/latex] = 18%<\/li>\n<li>P(J = 1-33 \u222a W \u2264 200) = [latex]\\dfrac{17}{50} + \\dfrac{22}{50}- \\dfrac{9}{50} = \\dfrac{30}{50}[\/latex] = 60%<\/li>\n<li>P(J = 1-33 | W \u2264 200) = [latex]\\dfrac{\\text{P}(\\text{J}-33\\cap\\text{W}\\leq200)}{\\text{P}(\\text{W}\\leq200)}=\\dfrac{0.18}{0.44}[\/latex] = 40.9%<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-224-1\">Data source: Yukon Bureau of Statistics. (2016). <em>Yukon Census historical population, 1901 to 2016<\/em>. https:\/\/yukon.ca\/sites\/yukon.ca\/files\/ybs\/fin-yukon-census-historical-population-1901-2016.pdf.\u00a0 <a href=\"#return-footnote-224-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-224-2\">Data source: Edmonton Elks. (n.d.). <em>Roster<\/em>. https:\/\/www.goelks.com\/roster\/ <a href=\"#return-footnote-224-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":123,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-224","chapter","type-chapter","status-publish","hentry"],"part":69,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/224","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/users\/123"}],"version-history":[{"count":5,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/224\/revisions"}],"predecessor-version":[{"id":325,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/224\/revisions\/325"}],"part":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/parts\/69"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapters\/224\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/media?parent=224"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/pressbooks\/v2\/chapter-type?post=224"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/contributor?post=224"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/busstatsancillary\/wp-json\/wp\/v2\/license?post=224"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}