{"id":220718,"date":"2025-05-28T17:04:04","date_gmt":"2025-05-28T17:04:04","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=220718"},"modified":"2025-05-28T17:05:25","modified_gmt":"2025-05-28T17:05:25","slug":"a-security-alarm-requires-a-four-digit-code","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/28\/a-security-alarm-requires-a-four-digit-code\/","title":{"rendered":"A security alarm requires a four-digit code"},"content":{"rendered":"\n

A security alarm requires a four-digit code. The code can use the digits 0\u20139 and the digits cannot be repeated.<\/p>\n\n\n\n

Which expression can be used to determine the probability of the alarm code beginning with a number greater than 7?<\/p>\n\n\n\n

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

Correct Answer:<\/strong> 2\u00d79\u00d78\u00d7710\u00d79\u00d78\u00d77\\frac{2 \\times 9 \\times 8 \\times 7}{10 \\times 9 \\times 8 \\times 7}<\/p>\n\n\n\n

\n\n\n\n

Explanation <\/strong><\/p>\n\n\n\n

We are given a four-digit security alarm code that uses digits from 0 to 9 without repetition<\/strong>, and we are asked to find the probability<\/strong> that the code begins with a number greater than 7<\/strong>.<\/p>\n\n\n\n

Step 1: Total number of possible 4-digit codes (no repetition)<\/h3>\n\n\n\n

The total number of 4-digit codes using digits 0\u20139 without repetition is:<\/p>\n\n\n\n

    \n
  • First digit: 10 options (0\u20139)<\/li>\n\n\n\n
  • Second digit: 9 options (one digit used already)<\/li>\n\n\n\n
  • Third digit: 8 options<\/li>\n\n\n\n
  • Fourth digit: 7 options<\/li>\n<\/ul>\n\n\n\n

    So, the total number of possible codes is: 10\u00d79\u00d78\u00d7710 \\times 9 \\times 8 \\times 7<\/p>\n\n\n\n

    Step 2: Favorable outcomes \u2014 codes starting with a digit > 7<\/h3>\n\n\n\n

    Digits greater than 7 are 8 and 9<\/strong> \u2014 that gives us 2 choices<\/strong> for the first digit.<\/p>\n\n\n\n

    Once the first digit is selected (either 8 or 9), we have:<\/p>\n\n\n\n

      \n
    • Second digit: 9 choices (excluding the first digit)<\/li>\n\n\n\n
    • Third digit: 8 choices (excluding the first two digits)<\/li>\n\n\n\n
    • Fourth digit: 7 choices<\/li>\n<\/ul>\n\n\n\n

      So, favorable outcomes: 2\u00d79\u00d78\u00d772 \\times 9 \\times 8 \\times 7<\/p>\n\n\n\n

      Step 3: Compute probability<\/h3>\n\n\n\n

      Probability = Favorable outcomes \u00f7 Total outcomes Probability=2\u00d79\u00d78\u00d7710\u00d79\u00d78\u00d77\\text{Probability} = \\frac{2 \\times 9 \\times 8 \\times 7}{10 \\times 9 \\times 8 \\times 7}<\/p>\n\n\n\n

      Notice that the common terms (9 \u00d7 8 \u00d7 7) cancel out: 210=0.2\\frac{2}{10} = 0.2<\/p>\n\n\n\n

      Thus, the probability that a randomly selected 4-digit code with no repeated digits begins with a digit greater than 7 is 0.2<\/strong>, or 20%<\/strong>.<\/p>\n\n\n\n

      The given expression correctly models this probability and highlights the importance of identifying constraints (no repetition) and specific conditions (first digit > 7) in probability problems.<\/p>\n\n\n\n

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

      A security alarm requires a four-digit code. The code can use the digits 0\u20139 and the digits cannot be repeated. Which expression can be used to determine the probability of the alarm code beginning with a number greater than 7? The Correct Answer and Explanation is: Correct Answer: 2\u00d79\u00d78\u00d7710\u00d79\u00d78\u00d77\\frac{2 \\times 9 \\times 8 \\times 7}{10 […]<\/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-220718","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220718","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=220718"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220718\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=220718"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=220718"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=220718"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}