{"id":197126,"date":"2025-03-06T16:57:52","date_gmt":"2025-03-06T16:57:52","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=197126"},"modified":"2025-03-06T16:57:54","modified_gmt":"2025-03-06T16:57:54","slug":"computer-keyboard-failures-can-be-attributed-to-electrical-effects-or-mechanical-defects","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/06\/computer-keyboard-failures-can-be-attributed-to-electrical-effects-or-mechanical-defects\/","title":{"rendered":"Computer keyboard failures can be attributed to electrical effects or mechanical defects"},"content":{"rendered":"\n

Computer keyboard failures can be attributed to electrical effects or mechanical defects. A repair company currently has 25 failed keyboards, 6 of which have electrical defects and 19 of which have mechanical defects.<\/p>\n\n\n\n

(a) How many ways are there to randomly select 6 of these keyboards for a thorough inspection (without regard to order)? 277100 ways<\/p>\n\n\n\n

(b) In how many ways can a sample of 6 keyboards be selected so that exactly two have an electrical defect? 19830 ways<\/p>\n\n\n\n

(c) If a sample of keyboards is randomly selected, what is the probability that at least one of these will be a mechanical defect? [Round your answer to four decimal places] 0.5471<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

The correct probability that at least one of the selected keyboards will have a mechanical defect is 1.0000<\/strong>, not 0.5471<\/strong>.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

We are given 25 failed keyboards, with:<\/p>\n\n\n\n

    \n
  • 6 having electrical defects<\/li>\n\n\n\n
  • 19 having mechanical defects<\/li>\n<\/ul>\n\n\n\n

    We need to determine the probability that a randomly selected sample of 6 keyboards contains at least one<\/strong> mechanical defect.<\/p>\n\n\n\n

    Step 1: Define the Probability Formula<\/strong>
    The easiest way to calculate this probability is to use the complement rule:
    [
    P(\\text{at least one mechanical defect}) = 1 – P(\\text{no mechanical defects})
    ]
    where ( P(\\text{no mechanical defects}) ) is the probability that all selected keyboards have electrical defects.<\/p>\n\n\n\n

    Step 2: Compute the Probability of No Mechanical Defects<\/strong>
    If all selected keyboards have electrical defects, then all 6 keyboards must be chosen from the 6 available electrical defect keyboards. The number of ways to choose all 6 from these 6 is:
    [
    \\text{Ways to choose 6 electrical keyboards} = \\binom{6}{6} = 1
    ]
    The number of ways to choose any 6 keyboards from the total of 25 is:
    [
    \\text{Total ways to choose 6 keyboards} = \\binom{25}{6} = 177100
    ]
    Thus, the probability of selecting only electrical defect keyboards is:
    [
    P(\\text{no mechanical defects}) = \\frac{1}{177100} \\approx 0.0000
    ]<\/p>\n\n\n\n

    Step 3: Compute the Probability of At Least One Mechanical Defect<\/strong>
    [
    P(\\text{at least one mechanical defect}) = 1 – 0.0000 = 1.0000
    ]<\/p>\n\n\n\n

    This means that whenever we randomly pick 6 keyboards, we are guaranteed to get at least one with a mechanical defect.<\/p>\n\n\n\n

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

    [
    \\mathbf{1.0000}
    ]<\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n

    The bar chart visually represents the probability of selecting at least one mechanical defect in the sample of keyboards. It highlights that the probability is effectively 1.0000<\/strong>, confirming that every randomly chosen sample of 6 keyboards will contain at least one with a mechanical defect.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Computer keyboard failures can be attributed to electrical effects or mechanical defects. A repair company currently has 25 failed keyboards, 6 of which have electrical defects and 19 of which have mechanical defects. (a) How many ways are there to randomly select 6 of these keyboards for a thorough inspection (without regard to order)? 277100 […]<\/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-197126","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/197126","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=197126"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/197126\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=197126"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=197126"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=197126"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}