{"id":273486,"date":"2025-07-27T13:43:04","date_gmt":"2025-07-27T13:43:04","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=273486"},"modified":"2025-07-27T13:43:12","modified_gmt":"2025-07-27T13:43:12","slug":"your-science-teacher-sets-up-six-flasks-5","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/27\/your-science-teacher-sets-up-six-flasks-5\/","title":{"rendered":"Your science teacher sets up six flasks.\u00a0"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-962.png\" alt=\"\" class=\"wp-image-273487\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The probability is&nbsp;<strong>14\/15<\/strong>.<\/p>\n\n\n\n<p>To solve this probability problem, it is easiest to first calculate the probability of the opposite event occurring and then subtract that result from 1. The opposite of &#8220;at least one reaction&#8221; is &#8220;no reaction at all.&#8221;<\/p>\n\n\n\n<p>A reaction only occurs when yeast is added to hydrogen peroxide. Therefore, for no reaction to occur, you must select the two flasks that contain only water.<\/p>\n\n\n\n<p>First, we need to determine the total number of ways to choose two flasks from the six available. Since the order in which the flasks are chosen does not matter, we use the combination formula, C(n, k) = n! \/ (k!(n-k)!), where n is the total number of items and k is the number you choose.<\/p>\n\n\n\n<p>The total number of ways to choose 2 flasks from 6 is:<br>C(6, 2) = 6! \/ (2! * (6-2)!) = 6! \/ (2! * 4!) = (6 * 5) \/ (2 * 1) = 15.<br>There are 15 possible pairs of flasks you can choose. This is the total number of possible outcomes.<\/p>\n\n\n\n<p>Next, we calculate the number of ways to choose two flasks that result in no reaction. This means we must choose both of the flasks containing water. There are 2 water flasks, so we need to find the number of ways to choose 2 flasks from those 2.<br>C(2, 2) = 2! \/ (2! * (2-2)!) = 2! \/ (2! * 0!) = 1.<br>There is only one way to select both water flasks. This is our favorable outcome for the &#8220;no reaction&#8221; event.<\/p>\n\n\n\n<p>The probability of no reaction is the number of ways to get no reaction divided by the total number of outcomes, which is 1\/15.<\/p>\n\n\n\n<p>Finally, the probability of at least one reaction is 1 minus the probability of no reaction:<br>P(at least one reaction) = 1 &#8211; P(no reaction) = 1 &#8211; 1\/15 = 14\/15.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-2295.jpeg\" alt=\"\" class=\"wp-image-273488\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: The probability is&nbsp;14\/15. To solve this probability problem, it is easiest to first calculate the probability of the opposite event occurring and then subtract that result from 1. The opposite of &#8220;at least one reaction&#8221; is &#8220;no reaction at all.&#8221; A reaction only occurs when yeast is added to [&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-273486","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/273486","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=273486"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/273486\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=273486"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=273486"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=273486"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}