{"id":133908,"date":"2023-03-11T23:28:19","date_gmt":"2023-03-11T17:58:19","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=133908"},"modified":"2023-03-11T23:28:19","modified_gmt":"2023-03-11T17:58:19","slug":"a-box-contains-10-tickets-2-of-which-carry-a-prize-of-7-8-each-5-of-which-carry-a-prize-of-3-4-each-and-remaining-3-carry-a-prize-of-2-each-if-one-ticket-is-drawn-at-random-find-the-mean-value","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/quiz\/a-box-contains-10-tickets-2-of-which-carry-a-prize-of-7-8-each-5-of-which-carry-a-prize-of-3-4-each-and-remaining-3-carry-a-prize-of-2-each-if-one-ticket-is-drawn-at-random-find-the-mean-value","title":{"rendered":"A box contains 10 tickets, 2 of which carry a prize of 7 8 each, 5 of which carry a prize of 3 4 each, and remaining 3 carry a prize of ? 2 each. If one ticket is drawn at random, find the mean value of the prize."},"content":{"rendered":"<h2>Question: A box contains 10 tickets, 2 of which carry a prize of 7 8 each, 5 of which carry a prize of 3 4 each, and remaining 3 carry a prize of ? 2 each. If one ticket is drawn at random, find the mean value of the prize.<\/h2>\n<p>&nbsp;<\/p>\n<h3>The correct answer is &#8211;<\/h3>\n<div class=\"group w-full text-gray-800 dark:text-gray-100 border-b border-black\/10 dark:border-gray-900\/50 bg-gray-50 dark:bg-[#444654]\">\n<div class=\"text-base gap-4 md:gap-6 md:max-w-2xl lg:max-w-2xl xl:max-w-3xl p-4 md:py-6 flex lg:px-0 m-auto\">\n<div class=\"relative flex w-[calc(100%-50px)] flex-col gap-1 md:gap-3 lg:w-[calc(100%-115px)]\">\n<div class=\"flex flex-grow flex-col gap-3\">\n<div class=\"min-h-[20px] flex flex-col items-start gap-4 whitespace-pre-wrap\">\n<div class=\"markdown prose w-full break-words dark:prose-invert light\">\n<p>To find the mean value of the prize, we need to first find the probability of drawing each type of ticket and then calculate the expected value of the prize.<\/p>\n<p>The probability of drawing a ticket with a prize of 7 8 is:<\/p>\n<p>P(7 8) = 2\/10 = 1\/5<\/p>\n<p>The probability of drawing a ticket with a prize of 3 4 is:<\/p>\n<p>P(3 4) = 5\/10 = 1\/2<\/p>\n<p>The probability of drawing a ticket with a prize of ? 2 is:<\/p>\n<p>P(? 2) = 3\/10<\/p>\n<p>Now we can calculate the expected value of the prize:<\/p>\n<p>E(prize) = P(7 8) x 7 8 + P(3 4) x 3 4 + P(? 2) x ? 2 E(prize) = (1\/5) x 7 8 + (1\/2) x 3 4 + (3\/10) x ? 2 E(prize) = 7\/20 + 3\/8 &#8211; 3\/50 E(prize) = 0.35 + 0.375 &#8211; 0.06 E(prize) = 0.665<\/p>\n<p>Therefore, the mean value of the prize is 0.665.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"flex justify-between\">\n<div class=\"text-gray-400 flex self-end lg:self-center justify-center mt-2 gap-3 md:gap-4 lg:gap-1 lg:absolute lg:top-0 lg:translate-x-full lg:right-0 lg:mt-0 lg:pl-2 visible\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Question: A box contains 10 tickets, 2 of which carry a prize of 7 8 each, 5 of which carry a prize of 3 4 each, and remaining 3 carry a prize of ? 2 each. If one ticket is drawn at random, find the mean value of the prize. &nbsp; The correct answer is [&hellip;]<\/p>\n","protected":false},"author":21842,"featured_media":132233,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12119],"tags":[],"class_list":{"0":"post-133908","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-quiz"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133908","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/users\/21842"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/comments?post=133908"}],"version-history":[{"count":1,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133908\/revisions"}],"predecessor-version":[{"id":133914,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133908\/revisions\/133914"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media\/132233"}],"wp:attachment":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media?parent=133908"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=133908"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=133908"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}