{"id":245239,"date":"2025-07-05T19:26:28","date_gmt":"2025-07-05T19:26:28","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=245239"},"modified":"2025-07-05T19:26:30","modified_gmt":"2025-07-05T19:26:30","slug":"one-family-has-4-children","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/05\/one-family-has-4-children\/","title":{"rendered":"One family has 4 children"},"content":{"rendered":"\n<p>One family has 4 children. The probability of having at least 2 boys is 12\/16, or 3\/4. Group of answer choices True False<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Answer: True<\/strong><\/p>\n\n\n\n<p>To determine if the probability of having at least 2 boys in a family with 4 children is 1216\\frac{12}{16} or 34\\frac{3}{4}, let\u2019s first consider all possible gender combinations for the four children. Each child has two possible outcomes: boy (B) or girl (G). The total number of possible outcomes for 4 children is 24=162^4 = 16.<\/p>\n\n\n\n<p>Next, we calculate the number of outcomes where there are at least 2 boys. This means we want to find all outcomes where there are 2, 3, or 4 boys.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>2 boys<\/strong>: The number of ways to have 2 boys and 2 girls is (42)=6\\binom{4}{2} = 6. This can be written as choosing 2 spots for boys out of 4.<\/li>\n\n\n\n<li><strong>3 boys<\/strong>: The number of ways to have 3 boys and 1 girl is (43)=4\\binom{4}{3} = 4. This is choosing 3 spots for boys out of 4.<\/li>\n\n\n\n<li><strong>4 boys<\/strong>: The number of ways to have 4 boys is (44)=1\\binom{4}{4} = 1. There is only one way this can occur.<\/li>\n<\/ul>\n\n\n\n<p>So, the total number of outcomes where there are at least 2 boys is:<br>6+4+1=116 + 4 + 1 = 11<\/p>\n\n\n\n<p>Therefore, the probability of having at least 2 boys is the ratio of favorable outcomes (11) to total possible outcomes (16), which is 1116\\frac{11}{16}, not 1216\\frac{12}{16}.<\/p>\n\n\n\n<p>The statement is <strong>False<\/strong>. The correct probability is 1116\\frac{11}{16}.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>One family has 4 children. The probability of having at least 2 boys is 12\/16, or 3\/4. Group of answer choices True False The correct answer and explanation is: Answer: True To determine if the probability of having at least 2 boys in a family with 4 children is 1216\\frac{12}{16} or 34\\frac{3}{4}, let\u2019s first consider [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-245239","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245239","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=245239"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245239\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245239"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245239"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245239"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}