{"id":185137,"date":"2025-01-22T06:56:03","date_gmt":"2025-01-22T06:56:03","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=185137"},"modified":"2025-01-22T06:56:05","modified_gmt":"2025-01-22T06:56:05","slug":"for-the-decision-tree","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/22\/for-the-decision-tree\/","title":{"rendered":"For the decision tree"},"content":{"rendered":"\n<p>For the decision tree in Figure 12.13, assume Chance Events E and F are independent.<\/p>\n\n\n\n<p>a. Draw the appropriate decision tree and calculate the EVPI for Chance Event E only.<\/p>\n\n\n\n<p>b. Draw the appropriate decision tree and calculate the EVPI for Chance Event F only.<\/p>\n\n\n\n<p>c. Draw the appropriate decision tree and calculate the EVPI for both Chance Events E and F: that is, perfect information for both E and F is available before a decision is made<\/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 determine the Expected Value of Perfect Information (EVPI) for Chance Events E and F in the decision tree, we follow these steps:<\/p>\n\n\n\n<p><strong>a. EVPI for Chance Event E Only<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Expected Monetary Value (EMV) without Perfect Information:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Decision A:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Outcomes:<\/li>\n\n\n\n<li>0.1 probability of 20<\/li>\n\n\n\n<li>0.2 probability of 10<\/li>\n\n\n\n<li>0.6 probability of 0<\/li>\n\n\n\n<li>0.1 probability of -10<\/li>\n\n\n\n<li>EMV(A) = (0.1 \u00d7 20) + (0.2 \u00d7 10) + (0.6 \u00d7 0) + (0.1 \u00d7 -10) = 2 + 2 + 0 &#8211; 1 = 3<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Decision B:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Outcomes:<\/li>\n\n\n\n<li>0.7 probability of 5<\/li>\n\n\n\n<li>0.3 probability of 1<\/li>\n\n\n\n<li>EMV(B) = (0.7 \u00d7 5) + (0.3 \u00d7 1) = 3.5 + 0.3 = 3.8<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Optimal decision without perfect information: <strong>Decision B<\/strong> with EMV = 3.8<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Expected Value with Perfect Information about E (EVwPI):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>With perfect information on E, choose the decision with the highest payoff for each outcome of E.<\/li>\n\n\n\n<li><strong>If E = 20:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Choose A (since 20 > 5)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>If E = 10:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Choose A (since 10 > 5)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>If E = 0:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Choose B (since 5 > 0)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>If E = -10:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Choose B (since 5 > -10)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>EVwPI = (0.1 \u00d7 20) + (0.2 \u00d7 10) + (0.6 \u00d7 5) + (0.1 \u00d7 5) = 2 + 2 + 3 + 0.5 = 7.5<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>EVPI for E:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>EVPI(E) = EVwPI &#8211; EMV(B) = 7.5 &#8211; 3.8 = 3.7<\/li>\n<\/ul>\n\n\n\n<p><strong>b. EVPI for Chance Event F Only<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Expected Monetary Value (EMV) without Perfect Information:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>As calculated above, EMV(A) = 3 and EMV(B) = 3.8<\/li>\n\n\n\n<li>Optimal decision without perfect information: <strong>Decision B<\/strong> with EMV = 3.8<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Expected Value with Perfect Information about F (EVwPI):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>With perfect information on F, choose the decision with the highest payoff for each outcome of F.<\/li>\n\n\n\n<li><strong>If F = 5:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Choose B (since 5 > 20, 10, 0, -10)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>If F = 1:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Choose B (since 1 > 20, 10, 0, -10)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>EVwPI = (0.7 \u00d7 5) + (0.3 \u00d7 1) = 3.5 + 0.3 = 3.8<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>EVPI for F:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>EVPI(F) = EVwPI &#8211; EMV(B) = 3.8 &#8211; 3.8 = 0<\/li>\n<\/ul>\n\n\n\n<p><strong>c. EVPI for Both Chance Events E and F<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Expected Value with Perfect Information about Both E and F (EVwPI):<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>With perfect information on both E and F, choose the decision with the highest payoff for each combination of E and F outcomes.<\/li>\n\n\n\n<li><strong>Combinations:<\/strong>\n<ul class=\"wp-block-list\">\n<li>E = 20, F = 5: Choose A (20 > 5)<\/li>\n\n\n\n<li>E = 20, F = 1: Choose A (20 > 1)<\/li>\n\n\n\n<li>E = 10, F = 5: Choose A (10 > 5)<\/li>\n\n\n\n<li>E = 10, F = 1: Choose A (10 > 1)<\/li>\n\n\n\n<li>E = 0, F = 5: Choose B (5 > 0)<\/li>\n\n\n\n<li>E = 0, F = 1: Choose B (5 > 0)<\/li>\n\n\n\n<li>E = -10, F = 5: Choose B (5 > -10)<\/li>\n\n\n\n<li>E = -10, F = 1: Choose B (5 > -10)<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Probabilities:<\/strong>\n<ul class=\"wp-block-list\">\n<li>P(E = 20) = 0.1<\/li>\n\n\n\n<li>P(E = 10) = 0.2<\/li>\n\n\n\n<li>P(E = 0) = 0.6<\/li>\n\n\n\n<li>P(E = -10) = 0.1<\/li>\n\n\n\n<li>P(F = 5) = 0.7<\/li>\n\n\n\n<li>P(F = 1) = 0.3<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Joint Probabilities (since E and F are independent):<\/strong>\n<ul class=\"wp-block-list\">\n<li>P(E = 20 and F = 5) = 0.1 \u00d7 0.7 = 0.07<\/li>\n\n\n\n<li>P<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>For the decision tree in Figure 12.13, assume Chance Events E and F are independent. a. Draw the appropriate decision tree and calculate the EVPI for Chance Event E only. b. Draw the appropriate decision tree and calculate the EVPI for Chance Event F only. c. Draw the appropriate decision tree and calculate the EVPI [&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-185137","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185137","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=185137"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185137\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=185137"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=185137"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=185137"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}