{"id":375,"date":"2017-04-30T13:11:12","date_gmt":"2017-04-30T17:11:12","guid":{"rendered":"http:\/\/www.blogs.euni.org\/?p=375"},"modified":"2017-04-30T13:11:12","modified_gmt":"2017-04-30T17:11:12","slug":"the-four-aces","status":"publish","type":"post","link":"https:\/\/www.blogs.euni.org\/?p=375","title":{"rendered":"The Four Aces"},"content":{"rendered":"<p>Fred was playing poker with his three friends Henry, John and Mack and had just dealt a hand for each.<\/p>\n<p>Fred saw that he had an Ace and wondered what the probability was that each of the other players also had an Ace.<\/p>\n<p>Later in the evening after the game, Fred decided to write a computer program that would deal ten thousand hands of poker to check how often four players each would be dealt an Ace.<\/p>\n<p>Then Fred wondered what would be the similar case for bridge hands dealt, for which purpose he changed a few input parameters for his computer program and received a surprise answer.<\/p>\n<p><em>On the average, how many of the ten thousand poker hand deals do you think resulted in an Ace for each player?<\/em><\/p>\n<p><em>On the average, how many bridge hand deals did Fred find gave an Ace to each player?<\/em><\/p>\n<div class=\"sharedaddy sd-sharing-enabled\"><div class=\"robots-nocontent sd-block sd-social sd-social-icon sd-sharing\"><h3 class=\"sd-title\">Share this:<\/h3><div class=\"sd-content\"><ul><li class=\"share-twitter\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"sharing-twitter-375\" class=\"share-twitter sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=375&amp;share=twitter\" target=\"_blank\" title=\"Click to share on Twitter\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on Twitter (Opens in new window)<\/span><\/a><\/li><li class=\"share-facebook\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"sharing-facebook-375\" class=\"share-facebook sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=375&amp;share=facebook\" target=\"_blank\" title=\"Click to share on Facebook\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on Facebook (Opens in new window)<\/span><\/a><\/li><li class=\"share-linkedin\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"sharing-linkedin-375\" class=\"share-linkedin sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=375&amp;share=linkedin\" target=\"_blank\" title=\"Click to share on LinkedIn\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on LinkedIn (Opens in new window)<\/span><\/a><\/li><li class=\"share-jetpack-whatsapp\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"\" class=\"share-jetpack-whatsapp sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=375&amp;share=jetpack-whatsapp\" target=\"_blank\" title=\"Click to share on WhatsApp\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on WhatsApp (Opens in new window)<\/span><\/a><\/li><li class=\"share-end\"><\/li><\/ul><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>Fred was playing poker with his three friends Henry, John and Mack and had just dealt a hand for each. Fred saw that he had an Ace and wondered what the probability was that each of the other players also had an Ace. Later in the evening after the game, Fred decided to write a [&hellip;]<\/p>\n<div class=\"sharedaddy sd-sharing-enabled\"><div class=\"robots-nocontent sd-block sd-social sd-social-icon sd-sharing\"><h3 class=\"sd-title\">Share this:<\/h3><div class=\"sd-content\"><ul><li class=\"share-twitter\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"sharing-twitter-375\" class=\"share-twitter sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=375&amp;share=twitter\" target=\"_blank\" title=\"Click to share on Twitter\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on Twitter (Opens in new window)<\/span><\/a><\/li><li class=\"share-facebook\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"sharing-facebook-375\" class=\"share-facebook sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=375&amp;share=facebook\" target=\"_blank\" title=\"Click to share on Facebook\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on Facebook (Opens in new window)<\/span><\/a><\/li><li class=\"share-linkedin\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"sharing-linkedin-375\" class=\"share-linkedin sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=375&amp;share=linkedin\" target=\"_blank\" title=\"Click to share on LinkedIn\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on LinkedIn (Opens in new window)<\/span><\/a><\/li><li class=\"share-jetpack-whatsapp\"><a rel=\"nofollow noopener noreferrer\" data-shared=\"\" class=\"share-jetpack-whatsapp sd-button share-icon no-text\" href=\"https:\/\/www.blogs.euni.org\/?p=375&amp;share=jetpack-whatsapp\" target=\"_blank\" title=\"Click to share on WhatsApp\"><span><\/span><span class=\"sharing-screen-reader-text\">Click to share on WhatsApp (Opens in new window)<\/span><\/a><\/li><li class=\"share-end\"><\/li><\/ul><\/div><\/div><\/div>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","jetpack_publicize_message":"","jetpack_is_tweetstorm":false},"categories":[14,10],"tags":[104],"jetpack_featured_media_url":"","jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7zDaf-63","jetpack-related-posts":[{"id":216,"url":"https:\/\/www.blogs.euni.org\/?p=216","url_meta":{"origin":375,"position":0},"title":"The First Ace","date":"September 20, 2016","format":false,"excerpt":"Pierre, the First Mate, was sitting in the mess room of the Nautilus flipping cards from a Tarot deck. He would periodically stop and write some numbers in a small notebook near the cards. \u201cWhat are you doing, First Mate?\u201d said Captain Nemo, who had stopped to look as he\u2026","rel":"","context":"In &quot;Combinations&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":900,"url":"https:\/\/www.blogs.euni.org\/?p=900","url_meta":{"origin":375,"position":1},"title":"The Dice Club Game","date":"April 27, 2019","format":false,"excerpt":"One Saturday afternoon, as Jack, now a full-fledged member, entered the Snake Eyes Dice Club in River City, he saw four persons throwing dice at a felt-covered table with Vince, the dealer. \u201cWhat\u2019s up today, Vince?\u201d asked Jack. \u201cLet me introduce you to Simon, Mary, Seamus and Henry here,\u201d said\u2026","rel":"","context":"In &quot;Algebra&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":865,"url":"https:\/\/www.blogs.euni.org\/?p=865","url_meta":{"origin":375,"position":2},"title":"The Four Card Deal","date":"February 13, 2019","format":false,"excerpt":"Jake dropped by the Happy Valley Card Club to see what was happening on a snowy winter\u2019s Friday evening in December. Jake enjoyed the conviviality and high-spirited discussions about the probabilities of card games in the lounge by the bar. Jake saw a large gathering around a large rectangular table,\u2026","rel":"","context":"In &quot;Number Theory&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":450,"url":"https:\/\/www.blogs.euni.org\/?p=450","url_meta":{"origin":375,"position":3},"title":"The Christmas Gifts","date":"August 31, 2017","format":false,"excerpt":"Fred and Mary were trying to work out how to give five gifts to their three boys for Christmas. The kids, Henry, Mark and Joe, had told them they wanted to receive gifts more or less at random this year to see how the gifts would be distributed. \u201cWe have\u2026","rel":"","context":"In &quot;Combinations&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":161,"url":"https:\/\/www.blogs.euni.org\/?p=161","url_meta":{"origin":375,"position":4},"title":"Some Special Numbers","date":"July 25, 2016","format":false,"excerpt":"A mathematician walking leisurely down a street on a Sunday afternoon spotted a colleague he had not seen for some time. \u201cHello Fred, nice to see you. \u201cLikewise, Leonard, I see you are well,\u201d replied Fred, shaking his hand. \u201cDid you ever marry Helen?\u201d \u201cYes, I did and now we\u2026","rel":"","context":"In &quot;Ages&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":862,"url":"https:\/\/www.blogs.euni.org\/?p=862","url_meta":{"origin":375,"position":5},"title":"The Three Cards","date":"January 30, 2019","format":false,"excerpt":"There was excitement again at the Happy Valley Card Club one Saturday afternoon. People were gathered around a table where a dealer was dealing three cards from a deck face down on the table, then, a bit later, three cards face up. Jake was curious and approached the dealer. \u201cHow\u2019s\u2026","rel":"","context":"In &quot;Combinations&quot;","img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/posts\/375"}],"collection":[{"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=375"}],"version-history":[{"count":2,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/posts\/375\/revisions"}],"predecessor-version":[{"id":377,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=\/wp\/v2\/posts\/375\/revisions\/377"}],"wp:attachment":[{"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=375"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=375"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.blogs.euni.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=375"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}