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Quantitative methods in Geography -<\/em> Discrete Probability Distributions<\/strong><\/span><\/p>\n\n

Discrete versus continuous events<\/span><\/p>\n\n

Discrete <\/em><\/strong>distributions - ex. binomial, geometric, Poisson (this week)<\/span><\/p>\n\n

versus Continuous <\/strong><\/em>distributions - ex. normal, exponential (next week)<\/span><\/p>\n\n

<\/p>\n"},"subContentId":"8b5cb9d9-5985-4dee-ab8e-59180f3d52f4","metadata":{"contentType":"Text","license":"U","title":"Untitled Text"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":4.357298474945534,"y":47.31182795698924,"width":52.50544662309368,"height":8.602150537634408,"action":{"library":"H5P.Link 1.3","params":{"linkWidget":{"protocol":"https:\/\/","url":"www.learner.org\/series\/against-all-odds-inside-statistics\/introduction-to-probability\/"},"title":"Please go and watch this 11 minute video about probability"},"metadata":{"contentType":"Link","license":"U"},"subContentId":"91d15423-60bb-4705-95a1-38c118470328"},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":61.00217864923747,"y":43.887741935483874,"width":37.58169934640523,"height":54.19354838709677,"action":{"library":"H5P.Image 1.1","params":{"contentName":"Image","alt":"Dogs","file":{"path":"images\/file-5f5e7c70de3bd.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":4000,"height":2915}},"subContentId":"2abcfc3a-cebb-434f-9672-5c77c16a3056","metadata":{"contentType":"Image","license":"U","title":"Untitled Image"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":26.438569206842924,"y":88.95705521472394,"width":32.65940902021773,"height":7.361963190184049,"action":{"library":"H5P.Audio 1.5","params":{"fitToWrapper":true,"playerMode":"full","controls":true,"autoplay":true,"playAudio":"Play audio","pauseAudio":"Pause audio","contentName":"Audio","audioNotSupported":"Your browser does not support this audio","files":[{"path":"audios\/files-5f610c4f25258.m4a","mime":"audio\/mp4","copyright":{"license":"U"}}]},"subContentId":"caf88490-dced-4532-95d2-343dff9d998c","metadata":{"contentType":"Audio","license":"U","title":"Untitled Audio"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}],"slideBackgroundSelector":{}},{"elements":[{"x":1.0893246187363834,"y":92.47311827956989,"width":44.66230936819172,"height":6.451612903225806,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Johnson, R. and Kuby, P. (2012) STAT2. <\/strong>Chapter 5.<\/p>\n"},"subContentId":"5abe3d6e-4b86-4f69-91dc-99eb76d7cc99","metadata":{"contentType":"Text","license":"U","title":"Untitled Text"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":1.0893246187363834,"y":2.1438172043010755,"width":46.84095860566449,"height":52.04301075268817,"action":{"library":"H5P.Image 1.1","params":{"contentName":"Image","file":{"path":"images\/file-5f5e70fd379e8.png","mime":"image\/png","copyright":{"license":"U"},"width":800,"height":450},"alt":"Random variables"},"subContentId":"23816229-d4cd-4b58-9aea-8a589076a227","metadata":{"contentType":"Image","license":"U","title":"Untitled Image"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":45.751633986928105,"y":38.58881720430107,"width":53.37690631808279,"height":59.56989247311827,"action":{"library":"H5P.Image 1.1","params":{"contentName":"Image","alt":"Discrete versus Continuous variables","title":"Discrete versus Continuous variables","file":{"path":"images\/file-5f5e711f13df2.png","mime":"image\/png","copyright":{"license":"U"},"width":800,"height":450}},"subContentId":"dd18b132-a2c4-4a24-9b6e-3a9436d03f48","metadata":{"contentType":"Image","license":"U","title":"Untitled Image"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":57.54276827371695,"y":15.337423312883436,"width":35.769828926905134,"height":7.361963190184049,"action":{"library":"H5P.Audio 1.5","params":{"fitToWrapper":true,"playerMode":"full","controls":true,"autoplay":true,"playAudio":"Play audio","pauseAudio":"Pause audio","contentName":"Audio","audioNotSupported":"Your browser does not support this audio","files":[{"path":"audios\/files-5f610f471eb75.m4a","mime":"audio\/mp4","copyright":{"license":"U"}}]},"subContentId":"cc343445-ed43-4370-b040-bfac9d57da73","metadata":{"contentType":"Audio","license":"U","title":"Untitled Audio"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}],"slideBackgroundSelector":{}},{"elements":[{"x":2.178649237472767,"y":90.32258064516128,"width":42.48366013071895,"height":6.451612903225806,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"

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Without replacement - *Draw1* :<\/strong> QS, 1D, 1C, QD & Draw2 : <\/strong>KH, 7D, 6D, KH & *Draw3* : <\/strong>QS, 7D, 6D, KS<\/p>\n"},"subContentId":"020b2d79-1f46-4cfa-aaed-0d3eb6871ff2","metadata":{"contentType":"Mark the Words","license":"U","title":"Untitled Mark the Words"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":2.178649237472767,"y":42.956989247311824,"width":31.59041394335512,"height":10.53763440860215,"action":{"library":"H5P.Shape 1.0","params":{"shape":{"fillColor":"#fff","borderWidth":"0","borderStyle":"solid","borderColor":"#000","borderRadius":"0"},"type":"rectangle","line":{"borderColor":"#000000","borderWidth":"1","borderStyle":"solid"}},"subContentId":"7dde7b48-be91-4b5e-b22c-652fbcbe5f7e","metadata":{"contentType":"Shapes","license":"U"}},"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false}],"slideBackgroundSelector":{}},{"elements":[{"x":83.87799564270152,"y":92.47311827956989,"width":13.071895424836601,"height":6.451612903225806,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Open Stax 3.2<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"78b9fd85-e1f8-433e-920a-0e6db88a3f0a"},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":37.03703703703704,"y":2.1438172043010755,"width":33.769063180827885,"height":49.89247311827957,"action":{"library":"H5P.Image 1.1","params":{"contentName":"Image","file":{"path":"images\/file-5f5e54e6bb3c3.png","mime":"image\/png","copyright":{"license":"U"},"width":600,"height":450},"alt":"Example"},"subContentId":"d459eb9d-eea9-4155-8565-fbaf789d04d4","metadata":{"contentType":"Image","license":"U","title":"Untitled Image"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":67.5363834422658,"y":44.03569892473118,"width":31.59041394335512,"height":46.666666666666664,"action":{"library":"H5P.Image 1.1","params":{"contentName":"Image","file":{"path":"images\/file-5f5e54f7d07ee.png","mime":"image\/png","copyright":{"license":"U"},"width":600,"height":450},"alt":"Example"},"subContentId":"466be723-fa2c-4e1b-b90d-2d347247b7c7","metadata":{"contentType":"Image","license":"U","title":"Untitled Image"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":0.4357298474945534,"y":2.150537634408602,"width":36.38344226579521,"height":53.76344086021505,"action":{"library":"H5P.Image 1.1","params":{"contentName":"Image","file":{"path":"images\/file-5f5e549188e0d.png","mime":"image\/png","copyright":{"license":"U"},"width":600,"height":450},"alt":"Mutually Exclusive Events","title":"Mutually Exclusive Events"},"metadata":{"contentType":"Image","license":"U","title":"Untitled Image"},"subContentId":"b3b51ff2-d7b9-417a-977c-347ec8b683fb"},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":3.1104199066874028,"y":88.95705521472394,"width":34.214618973561436,"height":7.361963190184049,"action":{"library":"H5P.Audio 1.5","params":{"fitToWrapper":true,"playerMode":"full","controls":true,"autoplay":true,"playAudio":"Play audio","pauseAudio":"Pause audio","contentName":"Audio","audioNotSupported":"Your browser does not support this audio","files":[{"path":"audios\/files-5f611a646d134.m4a","mime":"audio\/mp4","copyright":{"license":"U"}}]},"subContentId":"fb2903f3-ece9-413d-a954-857e40eac442","metadata":{"contentType":"Audio","license":"U","title":"Untitled Audio"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}],"slideBackgroundSelector":{}},{"elements":[{"x":59.912854030501094,"y":92.36559139784947,"width":37.03703703703704,"height":6.451612903225806,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Open Stax 3.3 Two basic rules of probability<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"52f84766-1a46-4b37-ba1c-1ac30c2e39c6"},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":1.0893246187363834,"y":81.72043010752688,"width":57.952069716775604,"height":6.451612903225806,"action":{"library":"H5P.Link 1.3","params":{"linkWidget":{"protocol":"https:\/\/","url":"www.learner.org\/series\/against-all-odds-inside-statistics\/probability-models\/"},"title":"Please watch this 10 1\/2 minute video about probability models"},"subContentId":"f615d9c7-deec-4664-a44e-8161b4d567cf","metadata":{"contentType":"Link","license":"U"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":47.276688453159046,"y":2.1438172043010755,"width":45.751633986928105,"height":67.74193548387096,"action":{"library":"H5P.Image 1.1","params":{"contentName":"Image","file":{"path":"images\/file-5f5e563fa44aa.png","mime":"image\/png","copyright":{"license":"U"},"width":600,"height":450},"alt":"The addition rule","title":"The addition rule"},"subContentId":"ed49a3e7-736a-4c34-83ee-1ed9cc764403","metadata":{"contentType":"Image","license":"U","title":"Untitled Image"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":1.0893246187363834,"y":2.1438172043010755,"width":45.751633986928105,"height":67.74193548387096,"action":{"library":"H5P.Image 1.1","params":{"contentName":"Image","file":{"path":"images\/file-5f5e5628e72b9.png","mime":"image\/png","copyright":{"license":"U"},"width":600,"height":450},"alt":"The multiplication rule","title":"The multiplication rule"},"subContentId":"6c5b61c3-f3e3-464f-862f-cf3ade0b527a","metadata":{"contentType":"Image","license":"U","title":"Untitled Image"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":25.05446623093682,"y":70.96774193548387,"width":51.19825708061002,"height":8.602150537634408,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Well this looks...horrible<\/em>. Lets look at some examples<\/p>\n"},"subContentId":"06ee81a7-7498-4195-8adb-e2015bba3465","metadata":{"contentType":"Text","license":"U","title":"Untitled Text"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":74.65007776049767,"y":46.01226993865031,"width":21.979112077573372,"height":40,"action":{"library":"H5P.Image 1.1","params":{"contentName":"Image","alt":"sad cat meme","file":{"path":"images\/file-5f611ab20260d.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":750,"height":691}},"subContentId":"fc799eb3-0a4f-4a37-876a-f9c5be77ea1e","metadata":{"contentType":"Image","license":"U","title":"Untitled Image"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":20.697167755991288,"y":88.17204301075269,"width":24.074074074074076,"height":5.161290322580645,"action":{"library":"H5P.Audio 1.5","params":{"fitToWrapper":true,"playerMode":"full","controls":true,"autoplay":true,"playAudio":"Play audio","pauseAudio":"Pause audio","contentName":"Audio","audioNotSupported":"Your browser does not support this audio","files":[{"path":"audios\/files-5f611f4ab8d3d.m4a","mime":"audio\/mp4","copyright":{"license":"U"}}]},"subContentId":"54e4289c-8a80-457c-856d-b0cf1b28beef","metadata":{"contentType":"Audio","license":"U","title":"Untitled Audio"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}],"slideBackgroundSelector":{}},{"elements":[{"x":2.178649237472767,"y":92.47311827956989,"width":13.071895424836601,"height":6.451612903225806,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Open Stax 3.3<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"16382568-447b-49a0-8161-acc6b65fceb4"},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":1.0893246187363834,"y":2.1438172043010755,"width":46.84095860566449,"height":69.24731182795698,"action":{"library":"H5P.Image 1.1","params":{"contentName":"Image","file":{"path":"images\/file-5f5e5659cefc8.png","mime":"image\/png","copyright":{"license":"U"},"width":600,"height":450},"alt":"Example"},"subContentId":"1d3d3e34-1f4e-4811-b8a2-e4babb6ac89f","metadata":{"contentType":"Image","license":"U","title":"Untitled Image"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":50.10893246187364,"y":3.225806451612903,"width":45.751633986928105,"height":67.74193548387096,"action":{"library":"H5P.Image 1.1","params":{"contentName":"Image","file":{"path":"images\/file-5f5e563fa44aa.png","mime":"image\/png","copyright":{"license":"U"},"width":600,"height":450},"alt":"The addition rule","title":"The addition rule"},"metadata":{"contentType":"Image","license":"U","title":"Untitled Image"},"subContentId":"54592263-6b0e-4115-8a88-28cff907052a"},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":15.686274509803923,"y":73.54838709677419,"width":21.78649237472767,"height":6.451612903225806,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Um, what just happened?<\/p>\n"},"subContentId":"66b8c68f-998a-4d41-8a2d-86be459ed378","metadata":{"contentType":"Text","license":"U","title":"Untitled Text"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":50.98039215686275,"y":71.82795698924731,"width":45.751633986928105,"height":27.311827956989244,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Oh yeah, I remember now! The UNION of two sets is a new set that contains all of the elements that are in at least one of the two sets. The union is written as A\u222aB. And more importantly, we get to use this simplified ADDITION RULE because of the mutual exclusivity of A and B.<\/p>\n"},"subContentId":"1de5a1a5-cd1c-4331-b6d3-fafeb0238127","metadata":{"contentType":"Text","license":"U","title":"Untitled Text"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":71.89542483660131,"y":40.86021505376344,"width":21.241830065359476,"height":26.021505376344084,"action":{"library":"H5P.Image 1.1","params":{"contentName":"Image","alt":"Union","file":{"path":"images\/file-5f611c680cd75.png","mime":"image\/png","copyright":{"license":"U"},"width":285,"height":177},"title":"Union"},"subContentId":"0661440b-92ff-460e-9102-ef56bb072fba","metadata":{"contentType":"Image","license":"U","title":"Untitled Image"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":51.19825708061002,"y":38.66258064516129,"width":21.0239651416122,"height":6.451612903225806,"action":{"library":"H5P.Shape 1.0","params":{"shape":{"fillColor":"rgba(255, 255, 255, 0)","borderWidth":"2","borderStyle":"solid","borderColor":"rgb(245, 16, 16)","borderRadius":"0"},"type":"rectangle","line":{"borderColor":"#000000","borderWidth":"1","borderStyle":"solid"}},"subContentId":"8c43ff0b-a19e-454f-94fc-db464782c853","metadata":{"contentType":"Shapes","license":"U"}},"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false}],"slideBackgroundSelector":{}},{"elements":[{"x":3.2679738562091503,"y":90.32258064516128,"width":13.071895424836601,"height":6.451612903225806,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Open Stax 3.3<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"16382568-447b-49a0-8161-acc6b65fceb4"},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":1.0893246187363834,"y":2.150537634408602,"width":46.514161220043576,"height":68.81720430107526,"action":{"library":"H5P.Image 1.1","params":{"contentName":"Image","file":{"path":"images\/file-5f5e566b23718.png","mime":"image\/png","copyright":{"license":"U"},"width":600,"height":450},"alt":"Example"},"subContentId":"2bd7ea5d-b690-4921-9728-f855aee98e15","metadata":{"contentType":"Image","license":"U","title":"Untitled Image"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":49.01960784313726,"y":2.150537634408602,"width":45.751633986928105,"height":67.74193548387096,"action":{"library":"H5P.Image 1.1","params":{"contentName":"Image","file":{"path":"images\/file-5f5e5628e72b9.png","mime":"image\/png","copyright":{"license":"U"},"width":600,"height":450},"alt":"The multiplication rule","title":"The multiplication rule"},"metadata":{"contentType":"Image","license":"U","title":"Untitled Image"},"subContentId":"8b98302b-7130-4d88-a59b-b9a7f39d8101"},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":10.893246187363834,"y":73.11827956989247,"width":23.965141612200437,"height":6.451612903225806,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Huh, what is going on here?<\/p>\n"},"subContentId":"72673dec-46fc-42ab-9564-3753f7a685a0","metadata":{"contentType":"Text","license":"U","title":"Untitled Text"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":43.57298474945534,"y":77.27827956989248,"width":54.46623093681917,"height":22.79569892473118,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Oh yeah, that simplified multiplication rule! The intersection of two sets is a new set that contains all of the elements that are in both sets. The intersection is written as A\u2229B. And more importantly, we get to use the simplified multiplication rule because of the INDEPENDENCE of A and B!<\/p>\n"},"subContentId":"9f046b9f-bbb5-4961-a0a1-767495854a49","metadata":{"contentType":"Text","license":"U","title":"Untitled Text"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":75.16339869281046,"y":45.107526881720425,"width":20.697167755991288,"height":32.68817204301075,"action":{"library":"H5P.Image 1.1","params":{"contentName":"Image","file":{"path":"images\/file-5f611d25624dd.jpg","mime":"image\/jpeg","copyright":{"license":"U"},"width":251,"height":201},"alt":"Intersection"},"subContentId":"04f7fdc1-490d-4dd9-960f-9f619b672a55","metadata":{"contentType":"Image","license":"U","title":"Untitled Image"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":50.871459694989106,"y":45.16129032258064,"width":21.0239651416122,"height":6.451612903225806,"action":{"library":"H5P.Shape 1.0","params":{"shape":{"fillColor":"rgba(255, 255, 255, 0)","borderWidth":"2","borderStyle":"solid","borderColor":"rgb(245, 16, 16)","borderRadius":"0"},"type":"rectangle","line":{"borderColor":"#000000","borderWidth":"1","borderStyle":"solid"}},"metadata":{"contentType":"Shapes","license":"U"},"subContentId":"79b29671-02b0-4cc5-abb8-330eee161b46"},"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false}],"slideBackgroundSelector":{}},{"elements":[{"x":0,"y":29.401935483870968,"width":100,"height":70.53763440860214,"action":{"library":"H5P.Shape 1.0","params":{"shape":{"fillColor":"#fff","borderWidth":"0","borderStyle":"solid","borderColor":"#000","borderRadius":"0"},"type":"rectangle","line":{"borderColor":"#000000","borderWidth":"1","borderStyle":"solid"}},"subContentId":"83187d12-3c29-45a7-b358-b9453b6e88c4","metadata":{"contentType":"Shapes","license":"U"}},"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false},{"x":0.5446623093681917,"y":0,"width":99.1285403050109,"height":90.32258064516128,"action":{"library":"H5P.Blanks 1.14","params":{"media":{"disableImageZooming":false},"text":"

Studies show that about 1 woman in 7 (approx. 14.3%) who live to be 90 will develop breast cancer. Suppose that of those women who develop breast cancer, a test is negative 2% of the time. Also suppose that in the general population of women the test for breast cancer is negative about 85% of the time. Let B = woman develops breast cancer and Let N = tests negative. Suppose one woman is selected at random. Fill in the missing values (use the addition and multiplication rules)<\/em><\/p>\n","overallFeedback":[{"from":0,"to":100}],"showSolutions":"Show solution","tryAgain":"Retry","checkAnswer":"Check","notFilledOut":"Please fill in all blanks to view solution","answerIsCorrect":"':ans' is correct","answerIsWrong":"':ans' is wrong","answeredCorrectly":"Answered correctly","answeredIncorrectly":"Answered incorrectly","solutionLabel":"Correct answer:","inputLabel":"Blank input @num of @total","inputHasTipLabel":"Tip available","tipLabel":"Tip","behaviour":{"enableRetry":true,"enableSolutionsButton":true,"enableCheckButton":true,"autoCheck":false,"caseSensitive":true,"showSolutionsRequiresInput":true,"separateLines":false,"confirmCheckDialog":false,"confirmRetryDialog":false,"acceptSpellingErrors":false},"scoreBarLabel":"You got :num out of :total points","confirmCheck":{"header":"Finish ?","body":"Are you sure you wish to finish ?","cancelLabel":"Cancel","confirmLabel":"Finish"},"confirmRetry":{"header":"Retry ?","body":"Are you sure you wish to retry ?","cancelLabel":"Cancel","confirmLabel":"Confirm"},"questions":["

a) What is the probability that the woman develops breast cancer? P(B) = *0.143* What is the probability that the woman tests negative? P(N) = *0.85* <\/p>\n\n

b) Given that the woman has breast cancer, what is the probability that she tests negative? P(N|B) = *0.02*<\/p>\n\n

c) What is the probability that the woman has breast cancer AND tests negative? P(B AND N) = *0.0029*<\/p>\n\n

d) What is the probability that the woman has breast cancer OR tests negative? P(B OR N) = *0.9901*<\/p>\n"]},"subContentId":"47445c94-9067-488e-8806-be53ae0d4519","metadata":{"contentType":"Fill in the Blanks","license":"U","title":"Untitled Fill in the Blanks"}},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""},{"x":84.9673202614379,"y":92.47311827956989,"width":13.071895424836601,"height":6.451612903225806,"action":{"library":"H5P.AdvancedText 1.1","params":{"text":"

Open Stax 3.3<\/p>\n"},"metadata":{"contentType":"Text","license":"U","title":"Untitled Text"},"subContentId":"2ac5edb4-164a-4fb7-a10d-dd349abd9213"},"alwaysDisplayComments":false,"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false,"solution":""}],"slideBackgroundSelector":{}},{"elements":[{"x":0,"y":29.401935483870965,"width":100,"height":70.53763440860214,"action":{"library":"H5P.Shape 1.0","params":{"shape":{"fillColor":"#fff","borderWidth":"0","borderStyle":"solid","borderColor":"#000","borderRadius":"0"},"type":"rectangle","line":{"borderColor":"#000000","borderWidth":"1","borderStyle":"solid"}},"metadata":{"contentType":"Shapes","license":"U"},"subContentId":"6b51b0b5-3fb4-48dd-b5a8-e957817bc8a0"},"backgroundOpacity":0,"displayAsButton":false,"buttonSize":"big","goToSlideType":"specified","invisible":false},{"x":0.8714596949891068,"y":3.010752688172043,"width":99.1285403050109,"height":75.26881720430107,"action":{"library":"H5P.Blanks 1.14","params":{"media":{"disableImageZooming":false},"text":"

e) Are having breast cancer and testing negative independent <\/em><\/strong>events? Yes or No = *No* : Consider, does P(N|B) = P(N)? This is a test of independence.<\/p>\n\n

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P(x=2) = *0.2466* :binompdf(100,8\/560,2) 4 digits after decimal<\/p>\n\n
P(x\u22646) = *0.9994* :binompdf(100,8\/560,6)<\/p>\n\n
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3 Quantitative methods in Geography - Discrete Probability distributions

Lisa Tutty