{"id":39524,"date":"2025-06-27T08:12:57","date_gmt":"2025-06-27T08:12:57","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=39524"},"modified":"2025-06-27T08:12:58","modified_gmt":"2025-06-27T08:12:58","slug":"a-standard-deck-of-52-playing-cards-contains-13-cards-in-each-of-four-suits","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-standard-deck-of-52-playing-cards-contains-13-cards-in-each-of-four-suits\/","title":{"rendered":"A standard deck of 52 playing cards contains 13 cards in each of four suits"},"content":{"rendered":"\n<p>A standard deck of 52 playing cards contains 13 cards in each of four suits: hearts, diamonds, clubs, and spades. Four cards are drawn from the deck at random. What is the approximate probability that exactly three of the cards are diamonds? 1% 4% 11% 44%<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer: 4%<\/strong><\/p>\n\n\n\n<p>To find the approximate probability that exactly three of the four randomly drawn cards are diamonds from a standard 52-card deck, we apply the concept of <strong>combinations<\/strong> and <strong>probability of compound events<\/strong>.<\/p>\n\n\n\n<p>A standard deck has 13 diamonds and 39 non-diamonds (from the remaining suits).<\/p>\n\n\n\n<p>We are selecting 4 cards such that exactly 3 are diamonds and 1 is not. This is a classic case of the <strong>hypergeometric distribution<\/strong>.<\/p>\n\n\n\n<p>The number of ways to choose exactly 3 diamonds from the 13 available is: (133)\\binom{13}{3}<\/p>\n\n\n\n<p>The number of ways to choose 1 non-diamond from the remaining 39 cards is: (391)\\binom{39}{1}<\/p>\n\n\n\n<p>So, the total favorable outcomes for our event (3 diamonds and 1 non-diamond) is: (133)\u00d7(391)\\binom{13}{3} \\times \\binom{39}{1}<\/p>\n\n\n\n<p>Now, we calculate the total number of ways to choose <strong>any<\/strong> 4 cards from the full deck: (524)\\binom{52}{4}<\/p>\n\n\n\n<p>Now plug in the values:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(133)=286\\binom{13}{3} = 286<\/li>\n\n\n\n<li>(391)=39\\binom{39}{1} = 39<\/li>\n\n\n\n<li>(524)=270725\\binom{52}{4} = 270725<\/li>\n<\/ul>\n\n\n\n<p>Favorable outcomes: 286\u00d739=11154286 \\times 39 = 11154<\/p>\n\n\n\n<p>Total outcomes: 270725270725<\/p>\n\n\n\n<p>Now, compute the probability: P=11154270725\u22480.0412&nbsp;or&nbsp;4.12%P = \\frac{11154}{270725} \\approx 0.0412 \\text{ or } 4.12\\%<\/p>\n\n\n\n<p>This gives an approximate probability of <strong>4%<\/strong>.<\/p>\n\n\n\n<p>This means that when drawing 4 cards at random from a standard deck, there is about a <strong>4% chance<\/strong> that exactly three of them will be diamonds and one will be from any other suit. This relatively low probability reflects the unlikelihood of such a specific outcome in a random draw.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A standard deck of 52 playing cards contains 13 cards in each of four suits: hearts, diamonds, clubs, and spades. Four cards are drawn from the deck at random. What is the approximate probability that exactly three of the cards are diamonds? 1% 4% 11% 44% The correct answer and explanation is: Correct Answer: 4% [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-39524","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39524","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=39524"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39524\/revisions"}],"predecessor-version":[{"id":39529,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/39524\/revisions\/39529"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=39524"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=39524"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=39524"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}