You Choose To Park Your Car In A Metered Parking Spot Where The Cost Of Parking For 1 Hour Is $1.50. The Cost Of A Parking Ticket Is $15. Historically, The Local Police Only Catch One Out Of Every 12 Parking Violators In A Given Hour. You Are Trying To Determine If It’s
What is the idea behind the question..?
Topic Parking probabilities and expected value calculations.
What is this question about..? This question presents a scenario where you have parked your car in a metered parking spot, and you need to weigh the cost of paying for parking versus risking a parking ticket. The question introduces the probability of getting caught by the local police, adding a layer of decision-making complexity to the problem.<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The question is about calculating the expected value of parking in a metered spot where you risk receiving a parking ticket, considering both the cost of paying for parking and the chance of getting caught. This is a typical problem in probability and expected value calculations, which are used to make decisions based on both risks and rewards.<\/p>\n\n\n\n The given information includes:<\/p>\n\n\n\n The expected value<\/strong> is a weighted average of all possible outcomes, taking into account both the costs and probabilities. The formula is:<\/p>\n\n\n\n [ Using the given numbers:<\/p>\n\n\n\n [ First, calculate the two components:<\/p>\n\n\n\n Now, add them together:<\/p>\n\n\n\n [ The expected value of parking for an hour in this scenario is $2.625<\/strong>. This means, on average, you would spend $2.625 when considering the possibility of receiving a parking ticket.<\/p>\n\n\n\n Based on this expected value calculation, you can decide whether it’s worth the risk of not paying the meter and possibly receiving a ticket. Since the expected cost of taking the risk ($2.625) is higher than simply paying the $1.50, it’s more economical to pay for the meter rather than risk a ticket.<\/p>\n\n\n\n In conclusion, the expected value calculation helps in making informed decisions by considering both the costs and probabilities involved in uncertain situations.<\/p>\n","protected":false},"excerpt":{"rendered":" You Choose To Park Your Car In A Metered Parking Spot Where The Cost Of Parking For 1 Hour Is $1.50. The Cost Of A Parking Ticket Is $15. Historically, The Local Police Only Catch One Out Of Every 12 Parking Violators In A Given Hour. You Are Trying To Determine If It’sWhat is the […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"","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-181779","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/181779","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=181779"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/181779\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=181779"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=181779"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=181779"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step-by-Step Breakdown<\/h3>\n\n\n\n
\n
Calculate Expected Value (EV)<\/h3>\n\n\n\n
EV = (P(\\text{Caught}) \\times \\text{Cost of Ticket}) + (P(\\text{Not Caught}) \\times \\text{Cost of Parking})
]<\/p>\n\n\n\n
EV = (0.0833 \\times 15) + (0.9167 \\times 1.50)
]<\/p>\n\n\n\n\n
EV = 1.25 + 1.375 = 2.625
]<\/p>\n\n\n\nInterpretation of the Expected Value<\/h3>\n\n\n\n
\n
Decision-Making<\/h3>\n\n\n\n