{"id":237915,"date":"2025-06-17T18:08:25","date_gmt":"2025-06-17T18:08:25","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=237915"},"modified":"2025-06-17T18:08:27","modified_gmt":"2025-06-17T18:08:27","slug":"a-bag-contains-30-lottery-ball-numbered-1-30","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/17\/a-bag-contains-30-lottery-ball-numbered-1-30\/","title":{"rendered":"A bag contains 30 lottery ball numbered 1-30."},"content":{"rendered":"\n

A bag contains 30 lottery ball numbered 1-30. A ball is selected, and NOT replaced, then another is drawn. what is the probability two perfect squares are chosen<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

We are given that a bag contains 30 lottery balls<\/strong>, numbered from 1 to 30<\/strong>. A ball is selected without replacement<\/strong>, then a second ball is selected. We are to find the probability that both selected balls are perfect squares<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

Step 1: Identify the perfect squares between 1 and 30<\/h3>\n\n\n\n

Perfect squares are numbers that are squares of whole numbers. Between 1 and 30, these are:<\/p>\n\n\n\n

    \n
  • 12=11^2 = 112=1<\/li>\n\n\n\n
  • 22=42^2 = 422=4<\/li>\n\n\n\n
  • 32=93^2 = 932=9<\/li>\n\n\n\n
  • 42=164^2 = 1642=16<\/li>\n\n\n\n
  • 52=255^2 = 2552=25<\/li>\n<\/ul>\n\n\n\n

    So, the perfect squares in this range are: 1, 4, 9, 16, 25<\/strong>.<\/p>\n\n\n\n

    This gives us 5 perfect square numbers<\/strong>.<\/p>\n\n\n\n

    \n\n\n\n

    Step 2: Find the total number of ways to draw 2 balls<\/h3>\n\n\n\n

    We are drawing 2 balls without replacement<\/strong> from a total of 30. The total number of possible outcomes is:30\u00d729=87030 \\times 29 = 87030\u00d729=870<\/p>\n\n\n\n

    \n\n\n\n

    Step 3: Find the number of favorable outcomes (drawing 2 perfect squares)<\/h3>\n\n\n\n

    There are 5 perfect square balls. We want to choose 2 of these in order, without replacement. So the number of favorable outcomes is:5\u00d74=205 \\times 4 = 205\u00d74=20<\/p>\n\n\n\n

    (We choose one of the 5 perfect square balls first, then one of the remaining 4.)<\/p>\n\n\n\n

    \n\n\n\n

    Step 4: Calculate the probability<\/h3>\n\n\n\n

    Probability=Favorable outcomesTotal outcomes=20870=287\\text{Probability} = \\frac{\\text{Favorable outcomes}}{\\text{Total outcomes}} = \\frac{20}{870} = \\frac{2}{87}Probability=Total outcomesFavorable outcomes\u200b=87020\u200b=872\u200b<\/p>\n\n\n\n

    \n\n\n\n

    Final Answer:<\/h3>\n\n\n\n

    287\\boxed{\\frac{2}{87}}872\u200b\u200b<\/p>\n\n\n\n

    \n\n\n\n

    Explanation:<\/h3>\n\n\n\n

    Probability measures how likely an event is to happen. In this case, we are looking at a specific type of event: selecting two perfect square-numbered balls from a group of 30, without replacing the first ball before drawing the second.<\/p>\n\n\n\n

    First, we identified the perfect squares between 1 and 30. Only five numbers qualify. Since we are selecting two balls and they are not replaced, the number of possible ordered pairs from 30 balls is 30 multiplied by 29.<\/p>\n\n\n\n

    From the 5 perfect squares, we can form 20 such ordered pairs where both numbers are perfect squares. Dividing the number of favorable outcomes by the total number of possible outcomes gives the desired probability.<\/p>\n\n\n\n

    This type of probability problem is an example of dependent events because the outcome of the first draw affects the possible outcomes of the second.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    A bag contains 30 lottery ball numbered 1-30. A ball is selected, and NOT replaced, then another is drawn. what is the probability two perfect squares are chosen The Correct Answer and Explanation is: We are given that a bag contains 30 lottery balls, numbered from 1 to 30. A ball is selected without replacement, […]<\/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-237915","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237915","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=237915"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237915\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=237915"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=237915"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=237915"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}