{"id":222894,"date":"2025-06-01T04:28:08","date_gmt":"2025-06-01T04:28:08","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=222894"},"modified":"2025-06-01T04:28:10","modified_gmt":"2025-06-01T04:28:10","slug":"your-science-teacher-sets-up-six-flasks-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/01\/your-science-teacher-sets-up-six-flasks-3\/","title":{"rendered":"Your science teacher sets up six flasks"},"content":{"rendered":"\n

Your science teacher sets up six flasks. Two of the flasks contain water and four of the flasks contain hydrogen peroxide. A reaction occurs when you add yeast to hydrogen peroxide. You add yeast to two of the flasks. What is the probability that at least one reaction will occur?
Your science teacher sets up six flasks. Two of the flasks contain water and four of the flasks contain hydrogen peroxide. A reaction occurs when you add yeast to hydrogen peroxide. You add yeast to two of the flasks. What is the probability that at least one reaction will occur?<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

\u2705 Correct Answer:<\/h3>\n\n\n\n

Probability = 13\/15<\/strong> or approximately 0.8667 (86.67%)<\/strong><\/p>\n\n\n\n

\n\n\n\n

\ud83e\uddea Explanation (Approximately 300 words):<\/h3>\n\n\n\n

To solve this problem, we are dealing with a probability scenario involving a favorable outcome: at least one reaction occurs<\/strong> when yeast is added to two randomly selected flasks out of six. Let\u2019s break it down:<\/p>\n\n\n\n

\n\n\n\n

\ud83d\udd22 Step 1: Understand the setup<\/h3>\n\n\n\n
    \n
  • Total number of flasks: 6<\/li>\n\n\n\n
  • Flasks with water (no reaction)<\/strong>: 2<\/li>\n\n\n\n
  • Flasks with hydrogen peroxide (reaction with yeast)<\/strong>: 4<\/li>\n\n\n\n
  • Yeast is added to 2 of the 6 flasks<\/strong><\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    \ud83c\udfaf Goal<\/h3>\n\n\n\n

    We want to calculate the probability that at least one of the two chosen flasks contains hydrogen peroxide<\/strong> (i.e., at least one reaction occurs).<\/p>\n\n\n\n

    Instead of calculating this directly, we use the complement rule<\/strong>:<\/p>\n\n\n\n

    \n

    <\/p>\n<\/blockquote>\n\n\n\n

    \\text{P(at least one reaction)} = 1 – \\text{P(no reaction)}
    ]<\/p>\n\n\n\n

    \n\n\n\n

    \u274c Step 2: Calculate P(no reaction)<\/h3>\n\n\n\n

    This happens only if both chosen flasks contain water<\/strong>, since yeast + water = no reaction.<\/p>\n\n\n\n

      \n
    • Number of ways to choose 2 flasks with only water<\/strong>: (22)=1\\binom{2}{2} = 1<\/li>\n\n\n\n
    • Total number of ways to choose any 2 flasks out of 6<\/strong>: (62)=15\\binom{6}{2} = 15<\/li>\n\n\n\n
    • So, P(no\u00a0reaction)=115\\text{P(no reaction)} = \\frac{1}{15}<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      \u2705 Step 3: Use Complement Rule<\/h3>\n\n\n\n

      P(at least one reaction)=1\u2212115=1415\\text{P(at least one reaction)} = 1 – \\frac{1}{15} = \\frac{14}{15}<\/p>\n\n\n\n

      \u26d4 Wait!<\/strong> Correction: Earlier we said 13\/15<\/strong>\u2014but upon rechecking:<\/p>\n\n\n\n

      If only 1 way out of 15 gives no reaction<\/strong>, then 14 ways give at least one reaction.<\/p>\n\n\n\n

      So the correct answer is:<\/p>\n\n\n\n

      \n

      <\/p>\n<\/blockquote>\n\n\n\n

      \\boxed{\\frac{14}{15} \\text{ or } 0.9333 \\text{ or } 93.33%}
      ]<\/p>\n\n\n\n

      \n\n\n\n

      \u2705 Final Answer:<\/h3>\n\n\n\n

      14\/15 or about 93.33%<\/strong><\/p>\n\n\n\n

      \ud83e\udde0 This means it’s very likely<\/strong> (93.33%) that you\u2019ll see at least one reaction when you randomly add yeast to two of the flasks.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      Your science teacher sets up six flasks. Two of the flasks contain water and four of the flasks contain hydrogen peroxide. A reaction occurs when you add yeast to hydrogen peroxide. You add yeast to two of the flasks. What is the probability that at least one reaction will occur?Your science teacher sets up six […]<\/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-222894","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/222894","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=222894"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/222894\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=222894"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=222894"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=222894"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}