An algebra 2 test has 5 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 5 questions, what is the probability that you get at least 1 question correct<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To find the probability that you get at least one question correct when randomly guessing on each of the 5 multiple choice questions, let’s break it down:<\/p>\n\n\n\n To find the probability of getting at least one question correct, it’s easier to first calculate the probability of the complementary event\u2014getting no<\/em> questions correct.<\/p>\n\n\n\n The probability of getting one question incorrect is ( \\frac{3}{4} ). For all 5 questions, since they are independent, the probability of getting all 5 questions incorrect is: The probability of getting at least one question correct is the complement of the probability of getting all questions incorrect: The probability of getting at least one question correct when guessing randomly on all 5 questions is approximately 0.7627<\/strong> or 76.27%<\/strong>.<\/p>\n\n\n\n In probability, the complement rule is often used when calculating the probability of “at least one” event happening. In this case, instead of calculating the probability of getting one, two, or more questions correct, we first calculate the easier-to-compute probability of getting zero questions correct and subtract that from 1. This approach simplifies the problem and leads us to the correct answer.<\/p>\n","protected":false},"excerpt":{"rendered":" An algebra 2 test has 5 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 5 questions, what is the probability that you get at least 1 question correct The Correct Answer and Explanation is: To find the probability that you get at least […]<\/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-162833","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/162833","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=162833"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/162833\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=162833"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=162833"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=162833"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Understand the setup<\/h3>\n\n\n\n
\n
[
P(\\text{correct}) = \\frac{1}{4}
]<\/li>\n\n\n\n
[
P(\\text{incorrect}) = 1 – \\frac{1}{4} = \\frac{3}{4}
]<\/li>\n\n\n\nStep 2: Calculate the probability of getting no<\/em> questions correct<\/h3>\n\n\n\n
[
P(\\text{all incorrect}) = \\left( \\frac{3}{4} \\right)^5
]
Now, calculate this value:
[
\\left( \\frac{3}{4} \\right)^5 = \\frac{243}{1024} \\approx 0.2373
]
So, the probability of getting all 5 questions incorrect is about 0.2373.<\/p>\n\n\n\nStep 3: Calculate the probability of getting at least one question correct<\/h3>\n\n\n\n
[
P(\\text{at least 1 correct}) = 1 – P(\\text{all incorrect}) = 1 – \\frac{243}{1024} = \\frac{781}{1024}
]
This simplifies to approximately:
[
P(\\text{at least 1 correct}) \\approx 0.7627
]<\/p>\n\n\n\nFinal Answer<\/h3>\n\n\n\n
Explanation<\/h3>\n\n\n\n