{"id":265764,"date":"2025-07-22T08:39:18","date_gmt":"2025-07-22T08:39:18","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=265764"},"modified":"2025-07-22T08:39:21","modified_gmt":"2025-07-22T08:39:21","slug":"it-has-been-estimated-that-about-30-of-frozen-chicken-contain-enough-salmonella-bacteria-to-cause-illness-if-improperly-cooked-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/22\/it-has-been-estimated-that-about-30-of-frozen-chicken-contain-enough-salmonella-bacteria-to-cause-illness-if-improperly-cooked-2\/","title":{"rendered":"It has been estimated that about 30% of frozen chicken contain enough salmonella bacteria to cause illness if improperly cooked."},"content":{"rendered":"\n<p><br>It has been estimated that about 30% of frozen chicken contain enough salmonella bacteria to cause illness if improperly cooked. A consumer purchases 12 frozen chickens. What is the probability that the consumer will have less than 2 contaminated chickens? Round to 3 decimal places.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>This problem can be modeled using a <strong>binomial distribution<\/strong>, as there are only two outcomes for each chicken: either it is contaminated or it is not. The binomial distribution formula is:P(X=k)=(nk)pk(1\u2212p)n\u2212kP(X = k) = \\binom{n}{k} p^k (1 &#8211; p)^{n &#8211; k}P(X=k)=(kn\u200b)pk(1\u2212p)n\u2212k<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>n=12n = 12n=12 is the number of trials (chickens),<\/li>\n\n\n\n<li>p=0.30p = 0.30p=0.30 is the probability of a chicken being contaminated,<\/li>\n\n\n\n<li>kkk is the number of contaminated chickens (which we are interested in, specifically less than 2).<\/li>\n<\/ul>\n\n\n\n<p>We are asked to find the probability that fewer than 2 chickens are contaminated, i.e., P(X&lt;2)P(X &lt; 2)P(X&lt;2). This is the sum of probabilities for X=0X = 0X=0 and X=1X = 1X=1:P(X&lt;2)=P(X=0)+P(X=1)P(X &lt; 2) = P(X = 0) + P(X = 1)P(X&lt;2)=P(X=0)+P(X=1)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Calculate P(X=0)P(X = 0)P(X=0)<\/h3>\n\n\n\n<p>The probability of having 0 contaminated chickens is:P(X=0)=(120)(0.30)0(0.70)12=1\u00d71\u00d7(0.70)12\u22480.0138P(X = 0) = \\binom{12}{0} (0.30)^0 (0.70)^{12} = 1 \\times 1 \\times (0.70)^{12} \\approx 0.0138P(X=0)=(012\u200b)(0.30)0(0.70)12=1\u00d71\u00d7(0.70)12\u22480.0138<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Calculate P(X=1)P(X = 1)P(X=1)<\/h3>\n\n\n\n<p>The probability of having exactly 1 contaminated chicken is:P(X=1)=(121)(0.30)1(0.70)11=12\u00d70.30\u00d7(0.70)11\u22480.0595P(X = 1) = \\binom{12}{1} (0.30)^1 (0.70)^{11} = 12 \\times 0.30 \\times (0.70)^{11} \\approx 0.0595P(X=1)=(112\u200b)(0.30)1(0.70)11=12\u00d70.30\u00d7(0.70)11\u22480.0595<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Add the probabilities<\/h3>\n\n\n\n<p>Now, we sum these probabilities to find P(X&lt;2)P(X &lt; 2)P(X&lt;2):P(X&lt;2)=P(X=0)+P(X=1)=0.0138+0.0595=0.0733P(X &lt; 2) = P(X = 0) + P(X = 1) = 0.0138 + 0.0595 = 0.0733P(X&lt;2)=P(X=0)+P(X=1)=0.0138+0.0595=0.0733<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The probability that the consumer will have fewer than 2 contaminated chickens is approximately <strong>0.073<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>This solution applies the binomial distribution because the scenario involves multiple independent trials (chickens) where each trial has a fixed probability of success (chicken being contaminated). The key here was identifying that we needed to find the cumulative probability for having fewer than 2 contaminated chickens (i.e., X=0X = 0X=0 and X=1X = 1X=1).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1506.jpeg\" alt=\"\" class=\"wp-image-265765\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>It has been estimated that about 30% of frozen chicken contain enough salmonella bacteria to cause illness if improperly cooked. A consumer purchases 12 frozen chickens. What is the probability that the consumer will have less than 2 contaminated chickens? Round to 3 decimal places. The Correct Answer and Explanation is: This problem can be [&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-265764","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/265764","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=265764"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/265764\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=265764"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=265764"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=265764"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}