{"id":683,"date":"2021-08-13T16:41:59","date_gmt":"2021-08-13T16:41:59","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=683"},"modified":"2023-12-05T09:04:54","modified_gmt":"2023-12-05T09:04:54","slug":"tree-and-venn-diagrams-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/tree-and-venn-diagrams-2\/","title":{"raw":"Venn Diagram","rendered":"Venn Diagram"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul id=\"list1523423\">\r\n \t<li>Draw a Venn diagram to represent a given scenario<\/li>\r\n \t<li>Use a Venn diagram to calculate probabilities<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2 data-type=\"title\">Venn Diagram<\/h2>\r\nA <strong>Venn diagram<\/strong> is a picture that represents the outcomes of an experiment. It generally consists of a box that represents the sample space S together with circles or ovals. The circles or ovals represent events.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSuppose an experiment has the outcomes [latex]1, 2, 3, ... , 12[\/latex] where each outcome has an equal chance of occurring. Let event [latex]A = \\{1, 2, 3, 4, 5, 6\\}[\/latex] and event [latex]B = \\{6, 7, 8, 9\\}[\/latex]. Then [latex] A \\text{ AND } B = \\{6\\}[\/latex] and [latex]A \\text{ OR }B = \\{1, 2, 3, 4, 5, 6, 7, 8, 9\\}[\/latex]. The Venn diagram is as follows:\r\n<figure id=\"eip-idm17287840\"><span id=\"id18119489\" data-type=\"media\" data-alt=\"A Venn diagram. An oval representing set A contains the values 1, 2, 3, 4, 5, and 6. An oval representing set B also contains the 6, along with 7, 8, and 9. The values 10, 11, and 12 are present but not contained in either set.\" data-display=\"block\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/132\/2016\/04\/21214409\/fig-ch03_06_01.jpg\" alt=\"A Venn diagram. An oval representing set A contains the values 1, 2, 3, 4, 5, and 6. An oval representing set B also contains the 6, along with 7, 8, and 9. The values 10, 11, and 12 are present but not contained in either set.\" width=\"380\" data-media-type=\"image\/png\" \/><\/span><\/figure>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nSuppose an experiment has outcomes black, white, red, orange, yellow, green, blue, and purple, where each outcome has an equal chance of occurring. Let event\u00a0<em data-effect=\"italics\">C<\/em>\u00a0= {green, blue, purple} and event\u00a0<em data-effect=\"italics\">P<\/em>\u00a0= {red, yellow, blue}. Then\u00a0<em data-effect=\"italics\">C<\/em>\u00a0AND\u00a0<em data-effect=\"italics\">P<\/em>\u00a0= {blue} and\u00a0<em data-effect=\"italics\">C<\/em>\u00a0OR\u00a0<em data-effect=\"italics\">P<\/em>\u00a0= {green, blue, purple, red, yellow}. Draw a Venn diagram representing this situation.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFlip two fair coins. Let [latex]A[\/latex] = tails on the first coin. Let [latex]B[\/latex] = tails on the second coin. Then [latex]A = \\{TT, TH\\}[\/latex] and [latex]B = \\{TT, HT\\}[\/latex]. Therefore,[latex]A \\text{ AND } B = \\{TT\\}[\/latex]. [latex]A \\text{ OR } B = \\{TH, TT, HT\\}[\/latex].\r\n\r\nThe sample space when you flip two fair coins is [latex]X = \\{HH, HT, TH, TT\\}[\/latex]. The outcome [latex]HH[\/latex] is in NEITHER [latex]A[\/latex] NOR [latex]B[\/latex]. The Venn diagram is as follows:\r\n<figure id=\"eip-idm154602320\"><span id=\"id18154607\" data-type=\"media\" data-alt=\"This is a venn diagram. An oval representing set A contains Tails + Heads and Tails + Tails. An oval representing set B also contains Tails + Tails, along with Heads + Tails. The universe S contains Heads + Heads, but this value is not contained in either set A or B.\" data-display=\"block\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/132\/2016\/04\/21214411\/fig-ch03_06_02.jpg\" alt=\"This is a venn diagram. An oval representing set A contains Tails + Heads and Tails + Tails. An oval representing set B also contains Tails + Tails, along with Heads + Tails. The universe S contains Heads + Heads, but this value is not contained in either set A or B.\" width=\"400\" data-media-type=\"image\/jpg\" \/><\/span><\/figure>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nRoll a fair, six-sided die. Let\u00a0<em data-effect=\"italics\">A<\/em>\u00a0= a prime number of dots is rolled. Let\u00a0<em data-effect=\"italics\">B<\/em>\u00a0= an odd number of dots is rolled. Then\u00a0<em data-effect=\"italics\">A<\/em>\u00a0= {2, 3, 5} and\u00a0<em data-effect=\"italics\">B<\/em>\u00a0= {1, 3, 5}. Therefore,\u00a0<em data-effect=\"italics\">A<\/em>\u00a0AND\u00a0<em data-effect=\"italics\">B<\/em>\u00a0= {3, 5}.\u00a0<em data-effect=\"italics\">A<\/em>\u00a0OR\u00a0<em data-effect=\"italics\">B<\/em>\u00a0= {1, 2, 3, 5}. The sample space for rolling a fair die is\u00a0<em data-effect=\"italics\">S<\/em>\u00a0= {1, 2, 3, 4, 5, 6}. Draw a Venn diagram representing this situation.\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Recall: Convert a Percent to a Decimal<\/h3>\r\n<ol>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Write the percent as a ratio with the denominator 100.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Convert the fraction to a decimal by dividing the numerator by the denominator.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nForty percent\u00a0of the students at a local college belong to a club and\u00a050%\u00a0work part time.\u00a0Five percent\u00a0of the students work part time and belong to a club. Draw a Venn diagram showing the relationships. Let\u00a0<em data-effect=\"italics\">C<\/em>\u00a0= student belongs to a club and\u00a0<em data-effect=\"italics\">PT<\/em>\u00a0= student works part time.<img class=\"wp-image-217 size-full aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/06\/13170529\/c42cfe1e3e08607ab0b459ae00b3448485a2c022.jpeg\" alt=\"This is a venn diagram with one set containing students in clubs and another set containing students working part-time. Both sets share students who are members of clubs and also work part-time. The universe is labeled S.\" width=\"488\" height=\"377\" \/>\r\n<p id=\"eip-827\" class=\" \">If a student is selected at random, find<\/p>\r\n\r\n<ul id=\"element-621\">\r\n \t<li>the probability that the student belongs to a club.\u00a0<em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">C<\/em>) = 0.40<\/li>\r\n \t<li>the probability that the student works part time.\u00a0<em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">PT<\/em>) = 0.50<\/li>\r\n \t<li>the probability that the student belongs to a club AND works part time.\u00a0<em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">C<\/em>\u00a0AND\u00a0<em data-effect=\"italics\">PT<\/em>) = 0.05<\/li>\r\n \t<li>the probability that the student belongs to a club\u00a0given\u00a0that the student works part time. [latex] P(C|PT)= \\frac{P(C \\ \\mathrm{AND} \\ PT)}{P(PT)} = \\frac{0.05}{0.50} = 0.1 [\/latex]<\/li>\r\n \t<li>the probability that the student belongs to a club\u00a0OR works part time.\u00a0<em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">C<\/em>\u00a0OR\u00a0<em data-effect=\"italics\">PT<\/em>) =\u00a0<em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">C<\/em>) +\u00a0<em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">PT<\/em>) -\u00a0<em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">C<\/em>\u00a0AND\u00a0<em data-effect=\"italics\">PT<\/em>) = 0.40 + 0.50 - 0.05 = 0.85<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nFifty percent of the workers at a factory work a second job, 25% have a spouse who also works, 5% work a second job and have a spouse who also works. Draw a Venn diagram showing the relationships. Let\u00a0<em data-effect=\"italics\">W<\/em>\u00a0= works a second job and\u00a0<em data-effect=\"italics\">S<\/em>\u00a0= spouse also works.\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Recall: The Mean<\/h3>\r\nThe mean of a set of n numbers is the arithmetic average of the numbers. It should be greater than the least number and less than the greatest number in the set.\r\n\r\n[latex]\\mathrm{Mean} = \\frac{\\mathrm{sum \\ of \\ values \\ in \\ the \\ set}}{n}[\/latex]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nA person with type O blood and a negative Rh factor (Rh-) can donate blood to any person with any blood type. Four percent of African Americans have type O blood and a negative RH factor, 5\u221210% of African Americans have the Rh- factor, and 51% have type O blood.\r\n\r\n<img class=\"alignnone wp-image-221 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/06\/13172201\/6358c71d71929c9e2a9e8b0ff23f34e5d54434e8.jpeg\" alt=\"This is an empty Venn diagram showing two overlapping circles. The left circle is labeled O and the right circle is labeled RH-.\" width=\"471\" height=\"354\" \/>\r\n<p id=\"fs-idp137061024\" class=\" \">The \u201cO\u201d circle represents the African Americans with type O blood. The \u201cRh-\u201c oval represents the African Americans with the Rh- factor.<\/p>\r\n<p id=\"fs-idp107178080\" class=\" \">We will take the average of 5% and 10% and use 7.5% as the percent of African Americans who have the Rh- factor. Let\u00a0<em data-effect=\"italics\">O<\/em>\u00a0= African American with Type O blood and\u00a0<em data-effect=\"italics\">R<\/em>\u00a0= African American with Rh- factor.<\/p>\r\n\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li><em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">O<\/em>) = ___________<\/li>\r\n \t<li><em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">R<\/em>) = ___________<\/li>\r\n \t<li><em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">O<\/em>\u00a0AND\u00a0<em data-effect=\"italics\">R<\/em>) = ___________<\/li>\r\n \t<li><em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">O<\/em>\u00a0OR\u00a0<em data-effect=\"italics\">R<\/em>) = ____________<\/li>\r\n \t<li>In the Venn Diagram, describe the overlapping area using a complete sentence.<\/li>\r\n \t<li>In the Venn Diagram, describe the area in the rectangle but outside both the circle and the oval using a complete sentence.<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"943970\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"943970\"]\r\n\r\na. 0.51; b. 0.075; c. 0.04; d. 0.545; e. The area represents the African Americans that have type O blood and the Rh- factor. f. The area represents the African Americans that have neither type O blood nor the Rh- factor.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n<p id=\"fs-idp200572912\" class=\" \">In a bookstore, the probability that the customer buys a novel is 0.6, and the probability that the customer buys a non-fiction book is 0.4. Suppose that the probability that the customer buys both is 0.2.<\/p>\r\n\r\n<ol id=\"fs-idp93717888\" type=\"a\">\r\n \t<li>Draw a Venn diagram representing the situation.<\/li>\r\n \t<li>Find the probability that the customer buys either a novel or a non-fiction book.<\/li>\r\n \t<li>In the Venn diagram, describe the overlapping area using a complete sentence.<\/li>\r\n \t<li>Suppose that some customers buy only compact disks. Draw an oval in your Venn diagram representing this event.<\/li>\r\n<\/ol>\r\n<\/div>\r\nhttps:\/\/youtu.be\/MassxXy8iko\r\n<div data-type=\"newline\" data-count=\"2\"><\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul id=\"list1523423\">\n<li>Draw a Venn diagram to represent a given scenario<\/li>\n<li>Use a Venn diagram to calculate probabilities<\/li>\n<\/ul>\n<\/div>\n<h2 data-type=\"title\">Venn Diagram<\/h2>\n<p>A <strong>Venn diagram<\/strong> is a picture that represents the outcomes of an experiment. It generally consists of a box that represents the sample space S together with circles or ovals. The circles or ovals represent events.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Suppose an experiment has the outcomes [latex]1, 2, 3, ... , 12[\/latex] where each outcome has an equal chance of occurring. Let event [latex]A = \\{1, 2, 3, 4, 5, 6\\}[\/latex] and event [latex]B = \\{6, 7, 8, 9\\}[\/latex]. Then [latex]A \\text{ AND } B = \\{6\\}[\/latex] and [latex]A \\text{ OR }B = \\{1, 2, 3, 4, 5, 6, 7, 8, 9\\}[\/latex]. The Venn diagram is as follows:<\/p>\n<figure id=\"eip-idm17287840\"><span id=\"id18119489\" data-type=\"media\" data-alt=\"A Venn diagram. An oval representing set A contains the values 1, 2, 3, 4, 5, and 6. An oval representing set B also contains the 6, along with 7, 8, and 9. The values 10, 11, and 12 are present but not contained in either set.\" data-display=\"block\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/132\/2016\/04\/21214409\/fig-ch03_06_01.jpg\" alt=\"A Venn diagram. An oval representing set A contains the values 1, 2, 3, 4, 5, and 6. An oval representing set B also contains the 6, along with 7, 8, and 9. The values 10, 11, and 12 are present but not contained in either set.\" width=\"380\" data-media-type=\"image\/png\" \/><\/span><\/figure>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Suppose an experiment has outcomes black, white, red, orange, yellow, green, blue, and purple, where each outcome has an equal chance of occurring. Let event\u00a0<em data-effect=\"italics\">C<\/em>\u00a0= {green, blue, purple} and event\u00a0<em data-effect=\"italics\">P<\/em>\u00a0= {red, yellow, blue}. Then\u00a0<em data-effect=\"italics\">C<\/em>\u00a0AND\u00a0<em data-effect=\"italics\">P<\/em>\u00a0= {blue} and\u00a0<em data-effect=\"italics\">C<\/em>\u00a0OR\u00a0<em data-effect=\"italics\">P<\/em>\u00a0= {green, blue, purple, red, yellow}. Draw a Venn diagram representing this situation.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Flip two fair coins. Let [latex]A[\/latex] = tails on the first coin. Let [latex]B[\/latex] = tails on the second coin. Then [latex]A = \\{TT, TH\\}[\/latex] and [latex]B = \\{TT, HT\\}[\/latex]. Therefore,[latex]A \\text{ AND } B = \\{TT\\}[\/latex]. [latex]A \\text{ OR } B = \\{TH, TT, HT\\}[\/latex].<\/p>\n<p>The sample space when you flip two fair coins is [latex]X = \\{HH, HT, TH, TT\\}[\/latex]. The outcome [latex]HH[\/latex] is in NEITHER [latex]A[\/latex] NOR [latex]B[\/latex]. The Venn diagram is as follows:<\/p>\n<figure id=\"eip-idm154602320\"><span id=\"id18154607\" data-type=\"media\" data-alt=\"This is a venn diagram. An oval representing set A contains Tails + Heads and Tails + Tails. An oval representing set B also contains Tails + Tails, along with Heads + Tails. The universe S contains Heads + Heads, but this value is not contained in either set A or B.\" data-display=\"block\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/132\/2016\/04\/21214411\/fig-ch03_06_02.jpg\" alt=\"This is a venn diagram. An oval representing set A contains Tails + Heads and Tails + Tails. An oval representing set B also contains Tails + Tails, along with Heads + Tails. The universe S contains Heads + Heads, but this value is not contained in either set A or B.\" width=\"400\" data-media-type=\"image\/jpg\" \/><\/span><\/figure>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Roll a fair, six-sided die. Let\u00a0<em data-effect=\"italics\">A<\/em>\u00a0= a prime number of dots is rolled. Let\u00a0<em data-effect=\"italics\">B<\/em>\u00a0= an odd number of dots is rolled. Then\u00a0<em data-effect=\"italics\">A<\/em>\u00a0= {2, 3, 5} and\u00a0<em data-effect=\"italics\">B<\/em>\u00a0= {1, 3, 5}. Therefore,\u00a0<em data-effect=\"italics\">A<\/em>\u00a0AND\u00a0<em data-effect=\"italics\">B<\/em>\u00a0= {3, 5}.\u00a0<em data-effect=\"italics\">A<\/em>\u00a0OR\u00a0<em data-effect=\"italics\">B<\/em>\u00a0= {1, 2, 3, 5}. The sample space for rolling a fair die is\u00a0<em data-effect=\"italics\">S<\/em>\u00a0= {1, 2, 3, 4, 5, 6}. Draw a Venn diagram representing this situation.<\/p>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Recall: Convert a Percent to a Decimal<\/h3>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Write the percent as a ratio with the denominator 100.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Convert the fraction to a decimal by dividing the numerator by the denominator.<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Forty percent\u00a0of the students at a local college belong to a club and\u00a050%\u00a0work part time.\u00a0Five percent\u00a0of the students work part time and belong to a club. Draw a Venn diagram showing the relationships. Let\u00a0<em data-effect=\"italics\">C<\/em>\u00a0= student belongs to a club and\u00a0<em data-effect=\"italics\">PT<\/em>\u00a0= student works part time.<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-217 size-full aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/06\/13170529\/c42cfe1e3e08607ab0b459ae00b3448485a2c022.jpeg\" alt=\"This is a venn diagram with one set containing students in clubs and another set containing students working part-time. Both sets share students who are members of clubs and also work part-time. The universe is labeled S.\" width=\"488\" height=\"377\" \/><\/p>\n<p id=\"eip-827\" class=\"\">If a student is selected at random, find<\/p>\n<ul id=\"element-621\">\n<li>the probability that the student belongs to a club.\u00a0<em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">C<\/em>) = 0.40<\/li>\n<li>the probability that the student works part time.\u00a0<em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">PT<\/em>) = 0.50<\/li>\n<li>the probability that the student belongs to a club AND works part time.\u00a0<em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">C<\/em>\u00a0AND\u00a0<em data-effect=\"italics\">PT<\/em>) = 0.05<\/li>\n<li>the probability that the student belongs to a club\u00a0given\u00a0that the student works part time. [latex]P(C|PT)= \\frac{P(C \\ \\mathrm{AND} \\ PT)}{P(PT)} = \\frac{0.05}{0.50} = 0.1[\/latex]<\/li>\n<li>the probability that the student belongs to a club\u00a0OR works part time.\u00a0<em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">C<\/em>\u00a0OR\u00a0<em data-effect=\"italics\">PT<\/em>) =\u00a0<em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">C<\/em>) +\u00a0<em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">PT<\/em>) &#8211;\u00a0<em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">C<\/em>\u00a0AND\u00a0<em data-effect=\"italics\">PT<\/em>) = 0.40 + 0.50 &#8211; 0.05 = 0.85<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Fifty percent of the workers at a factory work a second job, 25% have a spouse who also works, 5% work a second job and have a spouse who also works. Draw a Venn diagram showing the relationships. Let\u00a0<em data-effect=\"italics\">W<\/em>\u00a0= works a second job and\u00a0<em data-effect=\"italics\">S<\/em>\u00a0= spouse also works.<\/p>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Recall: The Mean<\/h3>\n<p>The mean of a set of n numbers is the arithmetic average of the numbers. It should be greater than the least number and less than the greatest number in the set.<\/p>\n<p>[latex]\\mathrm{Mean} = \\frac{\\mathrm{sum \\ of \\ values \\ in \\ the \\ set}}{n}[\/latex]<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>A person with type O blood and a negative Rh factor (Rh-) can donate blood to any person with any blood type. Four percent of African Americans have type O blood and a negative RH factor, 5\u221210% of African Americans have the Rh- factor, and 51% have type O blood.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-221 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/06\/13172201\/6358c71d71929c9e2a9e8b0ff23f34e5d54434e8.jpeg\" alt=\"This is an empty Venn diagram showing two overlapping circles. The left circle is labeled O and the right circle is labeled RH-.\" width=\"471\" height=\"354\" \/><\/p>\n<p id=\"fs-idp137061024\" class=\"\">The \u201cO\u201d circle represents the African Americans with type O blood. The \u201cRh-\u201c oval represents the African Americans with the Rh- factor.<\/p>\n<p id=\"fs-idp107178080\" class=\"\">We will take the average of 5% and 10% and use 7.5% as the percent of African Americans who have the Rh- factor. Let\u00a0<em data-effect=\"italics\">O<\/em>\u00a0= African American with Type O blood and\u00a0<em data-effect=\"italics\">R<\/em>\u00a0= African American with Rh- factor.<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li><em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">O<\/em>) = ___________<\/li>\n<li><em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">R<\/em>) = ___________<\/li>\n<li><em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">O<\/em>\u00a0AND\u00a0<em data-effect=\"italics\">R<\/em>) = ___________<\/li>\n<li><em data-effect=\"italics\">P<\/em>(<em data-effect=\"italics\">O<\/em>\u00a0OR\u00a0<em data-effect=\"italics\">R<\/em>) = ____________<\/li>\n<li>In the Venn Diagram, describe the overlapping area using a complete sentence.<\/li>\n<li>In the Venn Diagram, describe the area in the rectangle but outside both the circle and the oval using a complete sentence.<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q943970\">Show Solution<\/span><\/p>\n<div id=\"q943970\" class=\"hidden-answer\" style=\"display: none\">\n<p>a. 0.51; b. 0.075; c. 0.04; d. 0.545; e. The area represents the African Americans that have type O blood and the Rh- factor. f. The area represents the African Americans that have neither type O blood nor the Rh- factor.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p id=\"fs-idp200572912\" class=\"\">In a bookstore, the probability that the customer buys a novel is 0.6, and the probability that the customer buys a non-fiction book is 0.4. Suppose that the probability that the customer buys both is 0.2.<\/p>\n<ol id=\"fs-idp93717888\" type=\"a\">\n<li>Draw a Venn diagram representing the situation.<\/li>\n<li>Find the probability that the customer buys either a novel or a non-fiction book.<\/li>\n<li>In the Venn diagram, describe the overlapping area using a complete sentence.<\/li>\n<li>Suppose that some customers buy only compact disks. Draw an oval in your Venn diagram representing this event.<\/li>\n<\/ol>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Solving Problems with Venn Diagrams\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/MassxXy8iko?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div data-type=\"newline\" data-count=\"2\"><\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-683\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Statistics, Tree and Venn Diagrams. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/openstax.org\/books\/statistics\/pages\/3-5-tree-and-venn-diagrams\">https:\/\/openstax.org\/books\/statistics\/pages\/3-5-tree-and-venn-diagrams<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/statistics\/pages\/1-introduction<\/li><li>Introductory Statistics. <strong>Authored by<\/strong>: Barbara Illowsky, Susan Dean. <strong>Provided by<\/strong>: Open Stax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\">https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction<\/li><li>Prealgebra. <strong>Provided by<\/strong>: Open Stax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction\">https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">All rights reserved content<\/div><ul class=\"citation-list\"><li>Solving Problems with Venn Diagrams. <strong>Authored by<\/strong>: Mathispower4u. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/MassxXy8iko\">https:\/\/youtu.be\/MassxXy8iko<\/a>. <strong>License<\/strong>: <em>All Rights Reserved<\/em>. <strong>License Terms<\/strong>: Standard YouTube License<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":169134,"menu_order":22,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Statistics, Tree and Venn Diagrams\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/books\/statistics\/pages\/3-5-tree-and-venn-diagrams\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/statistics\/pages\/1-introduction\"},{\"type\":\"cc\",\"description\":\"Introductory Statistics\",\"author\":\"Barbara Illowsky, Susan Dean\",\"organization\":\"Open Stax\",\"url\":\"https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/introductory-statistics\/pages\/1-introduction\"},{\"type\":\"copyrighted_video\",\"description\":\"Solving Problems with Venn Diagrams\",\"author\":\"Mathispower4u\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/MassxXy8iko\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"Standard YouTube License\"},{\"type\":\"cc\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"Open Stax\",\"url\":\"https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/prealgebra\/pages\/1-introduction\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-683","chapter","type-chapter","status-publish","hentry"],"part":43,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/683","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/683\/revisions"}],"predecessor-version":[{"id":3521,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/683\/revisions\/3521"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/43"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/683\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=683"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=683"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=683"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=683"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}