What is the probability of drawing a king and a queen consecutively from a deck of 52 cards without replacement? Select one: \u03b1. 0.45 b. 0.7 c. 0.6 d. 0.55<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To calculate the probability of drawing a king and a queen consecutively from a standard 52-card deck without replacement, let’s break it down step by step.<\/p>\n\n\n\n None of the provided options (( \\alpha = 0.45 ), ( b = 0.7 ), ( c = 0.6 ), ( d = 0.55 )) are correct, as the actual probability (( \\approx 0.006 )) is much smaller. This may indicate an issue with the options in the question.<\/p>\n\n\n\n The probability is low because drawing a specific combination of two cards in a particular order from a deck of 52 cards is a rare event. With only 4 kings and 4 queens, the chances diminish further as the cards are drawn without replacement.<\/p>\n","protected":false},"excerpt":{"rendered":" What is the probability of drawing a king and a queen consecutively from a deck of 52 cards without replacement? Select one: \u03b1. 0.45 b. 0.7 c. 0.6 d. 0.55 The Correct Answer and Explanation is : To calculate the probability of drawing a king and a queen consecutively from a standard 52-card deck without […]<\/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-184244","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/184244","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=184244"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/184244\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=184244"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=184244"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=184244"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Understand the problem<\/h3>\n\n\n\n
\n
Step 2: Compute the probability<\/h3>\n\n\n\n
\n
[
P(\\text{King first}) = \\frac{\\text{Number of kings}}{\\text{Total cards}} = \\frac{4}{52}
]<\/li>\n\n\n\n
After drawing a king, 51 cards remain, and there are still 4 queens in the deck:
[
P(\\text{Queen second | King first}) = \\frac{\\text{Number of queens}}{\\text{Remaining cards}} = \\frac{4}{51}
]<\/li>\n\n\n\n
Multiply the probabilities of the two events since they are dependent:
[
P(\\text{King and then Queen}) = P(\\text{King first}) \\times P(\\text{Queen second | King first})
]
[
P(\\text{King and then Queen}) = \\frac{4}{52} \\times \\frac{4}{51} = \\frac{16}{2652} = \\frac{4}{663} \\approx 0.00603
]<\/li>\n<\/ol>\n\n\n\nStep 3: Match the options<\/h3>\n\n\n\n
Explanation<\/h3>\n\n\n\n