{"id":11017,"date":"2022-05-24T21:46:37","date_gmt":"2022-05-24T21:46:37","guid":{"rendered":"https:\/\/highclasswriters.com\/blog\/?p=11017"},"modified":"2022-05-24T21:46:38","modified_gmt":"2022-05-24T21:46:38","slug":"statistics-6","status":"publish","type":"post","link":"https:\/\/highclasswriters.com\/blog\/statistics-6\/","title":{"rendered":"statistics"},"content":{"rendered":"\n<p>In business (lotteries and casinos included), the owner wants to ensure that the business makes a profit.&nbsp; So that expected value (average profit) is always more than the expected loss (customer wins\/payout).&nbsp; Why would this be?&nbsp; This week we learn about the expected value (mean) of a probability distribution.&nbsp; This would apply to casinos, horse or car races, bets on athletic events, etc.&nbsp;<\/p>\n\n\n\n<p>Google your state&#8217;s (Virginia) Powerball or megamillions and calculate the probability of winning the jackpot. Most sites report odds instead of probability, so you&#8217;ll need to do a simple conversion.&nbsp;<\/p>\n\n\n\n<p>Share a link that takes us to the odds information on your state&#8217;s Powerball or megamillions.<\/p>\n\n\n\n<p><strong>In your original post<\/strong>, answer the following:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Create a probability table for this distribution<\/li><li>What is your expected gain or loss from playing?<\/li><li>If you played 100 times how much would you expect to win or lose?<\/li><li>After looking at this information and doing a few calculations, would you play?&nbsp; Why or why not?<\/li><li>Is it binomial?&nbsp; I&#8217;ll leave this for you to investigate and explain.<\/li><\/ul>\n\n\n\n<p><strong>In your responses to your classmates,&nbsp;<\/strong>address the following:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Would you play? Discuss in-depth.<\/li><li>How could the binomial distribution described in the original post be adjusted to favor the \u2018house\u2019 more? How could it be adjusted to favor the player more?\u201d<\/li><\/ul>\n\n\n\n<p>Convert the odds to a probability<br>To convert from odds to a probability, divide the odds by one plus the odds. So, to convert odds of 1\/9<br>to a probability, divide 1\/9 by 10\/9 to obtain the probability of 0.10.<br>Example:<br>Taking the odds of 1:9 and knowing I&#8217;ll win 1\/10 times I have a probability of .10 of winning.<br>This means I have a probability of .90 (the complement) of losing. Let&#8217;s say if I spend a dollar, I could<br>possibly win 2 dollars. If I lose, I lose the dollar.<br>My distribution looks like this.<br>X P(x)<br>-$1 .9 (lose)<br>$2 .1 (win)<br>Calculate expected value: E(x) = Sum (x* P(x))<br>E(x) = -1(.9) + 2(.1) = -.7 I expect to lose 70 cents ON AVERAGE each time I play.<br>If I play 100 times, I&#8217;ll lose .7(100) &#8212; expected loss in one game times the number of times I play<br>I expect to lose $70 dollars if I play 100 times. Why do I not expect to lose 100 dollars?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In business (lotteries and casinos included), the owner wants to ensure that the business makes a profit.&nbsp; So that expected [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","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":"","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":"var(--ast-global-color-4)","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":[1],"tags":[],"class_list":["post-11017","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>statistics - Highclasswriters<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/highclasswriters.com\/blog\/statistics-6\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"statistics - Highclasswriters\" \/>\n<meta property=\"og:description\" content=\"In business (lotteries and casinos included), the owner wants to ensure that the business makes a profit.&nbsp; 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