{"id":1032,"date":"2023-06-22T01:45:12","date_gmt":"2023-06-22T01:45:12","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/binomial-distribution-learn-it-1\/"},"modified":"2023-10-23T13:05:18","modified_gmt":"2023-10-23T13:05:18","slug":"binomial-distribution-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/binomial-distribution-learn-it-1\/","title":{"raw":"Binomial Distribution: Learn It 1","rendered":"Binomial Distribution: Learn It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Use a binomial distribution to calculate probability<\/li>\r\n\t<li>Determine if a probability model meets the conditions for a binomial distribution<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h3>Bernoulli Trial<\/h3>\r\n<p>A <strong>Bernoulli trial<\/strong> is a chance experiment with the following three properties:<\/p>\r\n<ul>\r\n\t<li>There are exactly two possible outcomes of the chance experiment. We label one of them as a <em>success<\/em> and the other as a <em>failure<\/em> (these aren\u2019t value judgments on the outcomes, just labels; usually, we call the outcome we\u2019re most interested in the <em>success<\/em> outcome).<\/li>\r\n\t<li>The probability of success is the same for every trial. We call <strong>the probability of success [latex]p[\/latex]<\/strong>. Since the only two outcomes are success and failure, the probability of failure is the probability that the trial does not result in a success, so we can use the NOT probability rule to find that <strong>the probability of failure is [latex]1-p[\/latex]<\/strong>.<\/li>\r\n\t<li>The trials are independent from one another. (This means that the outcome of one trial does not affect the likelihood of the possible outcomes of subsequent trials.)<\/li>\r\n<\/ul>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>binomial experiment<\/h3>\r\n<p>A <strong>binomial experiment<\/strong> is an experiment consisting of a fixed number, [latex]n[\/latex], of independent Bernoulli trials that counts the number of successes out of\u00a0[latex]n[\/latex]\u00a0trials. Notice that the number of successes in a binomial experiment is a discrete random variable.<\/p>\r\n<p>The distribution of this random variable is modeled with the <strong>binomial distribution<\/strong>.<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1021[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Use a binomial distribution to calculate probability<\/li>\n<li>Determine if a probability model meets the conditions for a binomial distribution<\/li>\n<\/ul>\n<\/section>\n<h3>Bernoulli Trial<\/h3>\n<p>A <strong>Bernoulli trial<\/strong> is a chance experiment with the following three properties:<\/p>\n<ul>\n<li>There are exactly two possible outcomes of the chance experiment. We label one of them as a <em>success<\/em> and the other as a <em>failure<\/em> (these aren\u2019t value judgments on the outcomes, just labels; usually, we call the outcome we\u2019re most interested in the <em>success<\/em> outcome).<\/li>\n<li>The probability of success is the same for every trial. We call <strong>the probability of success [latex]p[\/latex]<\/strong>. Since the only two outcomes are success and failure, the probability of failure is the probability that the trial does not result in a success, so we can use the NOT probability rule to find that <strong>the probability of failure is [latex]1-p[\/latex]<\/strong>.<\/li>\n<li>The trials are independent from one another. (This means that the outcome of one trial does not affect the likelihood of the possible outcomes of subsequent trials.)<\/li>\n<\/ul>\n<section class=\"textbox keyTakeaway\">\n<h3>binomial experiment<\/h3>\n<p>A <strong>binomial experiment<\/strong> is an experiment consisting of a fixed number, [latex]n[\/latex], of independent Bernoulli trials that counts the number of successes out of\u00a0[latex]n[\/latex]\u00a0trials. Notice that the number of successes in a binomial experiment is a discrete random variable.<\/p>\n<p>The distribution of this random variable is modeled with the <strong>binomial distribution<\/strong>.<\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1021\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1021&theme=lumen&iframe_resize_id=ohm1021&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":11,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":2912,"module-header":"learn_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1032"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":4,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1032\/revisions"}],"predecessor-version":[{"id":4079,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1032\/revisions\/4079"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/2912"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1032\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1032"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1032"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1032"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1032"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}