{"id":206589,"date":"2025-04-02T15:16:36","date_gmt":"2025-04-02T15:16:36","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=206589"},"modified":"2025-04-02T15:16:38","modified_gmt":"2025-04-02T15:16:38","slug":"an-ace-10-of-diamonds-or-2-of-spades-appears-in-drawing-a-single-card-from-a-well-shuffled-ordinary-deck-of-52-cards","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/04\/02\/an-ace-10-of-diamonds-or-2-of-spades-appears-in-drawing-a-single-card-from-a-well-shuffled-ordinary-deck-of-52-cards\/","title":{"rendered":"An ace, 10 of diamonds, or 2 of spades appears in drawing a single card from a well-shuffled ordinary deck of 52 cards"},"content":{"rendered":"\n<p>An ace, 10 of diamonds, or 2 of spades appears in drawing a single card from a well-shuffled ordinary deck of 52 cards.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To find the probability of drawing an ace, a 10 of diamonds, or a 2 of spades from a standard deck of 52 cards, we follow these steps:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Count Favorable Outcomes<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>There are <strong>4 aces<\/strong> (one in each suit: hearts, diamonds, clubs, and spades).<\/li>\n\n\n\n<li>There is <strong>1 ten of diamonds<\/strong>.<\/li>\n\n\n\n<li>There is <strong>1 two of spades<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>Since these events are mutually exclusive (they do not overlap), we simply add their probabilities.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Compute Probability<\/h3>\n\n\n\n<p>The probability of drawing an ace:<br>[<br>P(Ace) = \\frac{4}{52}<br>]<br>The probability of drawing a 10 of diamonds:<br>[<br>P(10\\ of\\ Diamonds) = \\frac{1}{52}<br>]<br>The probability of drawing a 2 of spades:<br>[<br>P(2\\ of\\ Spades) = \\frac{1}{52}<br>]<br>Adding these probabilities together:<br>[<br>P(Ace\\ or\\ 10\\ of\\ Diamonds\\ or\\ 2\\ of\\ Spades) = \\frac{4}{52} + \\frac{1}{52} + \\frac{1}{52} = \\frac{6}{52}<br>]<br>[<br>= \\frac{3}{26} \\approx 0.1154 \\text{ (or 11.54%)}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>The probability calculation is straightforward since the three outcomes (drawing an ace, a 10 of diamonds, or a 2 of spades) do not overlap. If they did, we would have to subtract their intersection. However, each card is unique, so their probabilities add directly.<\/p>\n\n\n\n<p>This method applies the <strong>addition rule of probability<\/strong>, which states that for mutually exclusive events, the probability of one occurring is the sum of their individual probabilities.<\/p>\n\n\n\n<p>Thus, the probability of drawing an ace, a 10 of diamonds, or a 2 of spades from a standard deck of 52 cards is <strong>3\/26 or 11.54%<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/04\/image-18.png\" alt=\"\" class=\"wp-image-206590\"\/><\/figure>\n\n\n\n<p>Here is the image generated using DALL\u00b7E, OpenAI&#8217;s legacy image-generation model. It visually represents the probability question with a deck of 52 cards spread out, highlighting the Ace of Spades, 10 of Diamonds, and 2 of Spades on a green felt poker table. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>An ace, 10 of diamonds, or 2 of spades appears in drawing a single card from a well-shuffled ordinary deck of 52 cards. The correct answer and explanation is : To find the probability of drawing an ace, a 10 of diamonds, or a 2 of spades from a standard deck of 52 cards, we [&hellip;]<\/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-206589","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206589","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=206589"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/206589\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=206589"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=206589"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=206589"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}