To determine the probability of choosing a specific color fingerboard, we first calculate the total number of fingerboards: Total Fingerboards=9(grey)+4(white)+3(yellow)=16\\text{Total Fingerboards} = 9 (\\text{grey}) + 4 (\\text{white}) + 3 (\\text{yellow}) = 16<\/p>\n\n\n\n
Now, we calculate the probability of each event:<\/p>\n\n\n\n
- \n
- Choosing a grey fingerboard<\/strong> P(grey)=916P(\\text{grey}) = \\frac{9}{16}<\/li>\n\n\n\n
- Choosing a white fingerboard<\/strong> P(white)=416=14P(\\text{white}) = \\frac{4}{16} = \\frac{1}{4}<\/li>\n\n\n\n
- Choosing a yellow fingerboard<\/strong> P(yellow)=316P(\\text{yellow}) = \\frac{3}{16}<\/li>\n<\/ol>\n\n\n\n
Since probability values range from 0 (impossible event) to 1 (certain event), we can represent these values on a number line.<\/p>\n\n\n\n
I’ll now generate an image illustrating the probability of these events on a number line.<\/p>\n\n\n\n
The image above visually represents the probabilities of selecting a grey, white, or yellow fingerboard on a number line.<\/p>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
- \n
- Understanding Probability<\/strong>
Probability quantifies the likelihood of an event occurring, given as a fraction or decimal between 0 and 1. Here, the total sample space consists of 16 fingerboards.<\/li>\n\n\n\n- Computing Each Probability<\/strong>\n
- \n
- Grey Fingerboard<\/strong>: Since there are 9 grey fingerboards out of 16, the probability is 9\/169\/16<\/strong> or approximately 0.5625<\/strong>.<\/li>\n\n\n\n
- White Fingerboard<\/strong>: With 4 white fingerboards, the probability is 4\/16=1\/44\/16 = 1\/4<\/strong> or 0.25<\/strong>.<\/li>\n\n\n\n
- Yellow Fingerboard<\/strong>: With 3 yellow fingerboards, the probability is 3\/163\/16<\/strong> or 0.1875<\/strong>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
- Placing Values on the Number Line<\/strong>\n
- \n
- Each probability is plotted on the number line ranging from 0 to 1.<\/li>\n\n\n\n
- The grey probability (9\/16) is closer to 0.56.<\/li>\n\n\n\n
- The white probability (1\/4) is 0.25.<\/li>\n\n\n\n
- The yellow probability (3\/16) is about 0.1875.<\/li>\n\n\n\n
- These values are marked with red dots for clarity.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
- Interpreting the Graph<\/strong>
The closer the probability is to 1, the more likely the event is. Since grey has the highest probability (9\/16), it is the most likely choice. White (1\/4) is the next likely, followed by yellow (3\/16), which has the lowest chance.<\/li>\n<\/ol>\n\n\n\nThis visualization makes it easy to compare the likelihood of each event.<\/p>\n\n\n\n
![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/03\/image-132-1024x388.png\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"David has a collection of 9 grey fingerboards, 4 white fingerboards, and 3 yellow fingerboards. He chooses one at random. Locate the probability of the following events on the number line. The correct answer and explanation is: To determine the probability of choosing a specific color fingerboard, we first calculate the total number of fingerboards: […]<\/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-196228","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196228","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=196228"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196228\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=196228"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=196228"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=196228"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- White Fingerboard<\/strong>: With 4 white fingerboards, the probability is 4\/16=1\/44\/16 = 1\/4<\/strong> or 0.25<\/strong>.<\/li>\n\n\n\n
- Computing Each Probability<\/strong>\n
- Choosing a white fingerboard<\/strong> P(white)=416=14P(\\text{white}) = \\frac{4}{16} = \\frac{1}{4}<\/li>\n\n\n\n