{"id":211695,"date":"2025-05-05T06:45:21","date_gmt":"2025-05-05T06:45:21","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=211695"},"modified":"2025-05-05T06:45:23","modified_gmt":"2025-05-05T06:45:23","slug":"in-the-game-of-keno-20-balls-are-selected-at-random-from-80-balls-numbered-1-80","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/05\/in-the-game-of-keno-20-balls-are-selected-at-random-from-80-balls-numbered-1-80\/","title":{"rendered":"In the game of keno, 20 balls are selected at random from 80 balls numbered 1\u201380"},"content":{"rendered":"\n

In the game of keno, 20 balls are selected at random from 80 balls numbered 1\u201380. a. Use Table I in Appendix A to simulate one game of keno by obtaining 20 random numbers between 1 and 80. Start at the two-digit number in line number 5 and column numbers 31\u201332, read down the column, up the next, and so on. b. If you have access to a random-number generator, use it to solve part<\/p>\n\n\n\n

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

Sure! Let’s go through part (a)<\/strong> of the question first \u2014 simulating one game of Keno<\/strong> using a random number table<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

\ud83d\udccc Part A: Simulate One Keno Game Using a Random Number Table<\/h3>\n\n\n\n

You are instructed to:<\/p>\n\n\n\n

    \n
  • Use Table I<\/strong> from Appendix A<\/strong> (usually in statistics textbooks),<\/li>\n\n\n\n
  • Start at line 5<\/strong>, columns 31\u201332<\/strong>,<\/li>\n\n\n\n
  • Read down the column<\/strong>, then up the next<\/strong>, alternating.<\/li>\n<\/ul>\n\n\n\n

    Since I don\u2019t have direct access to the physical table you have, let me simulate this step for you using an example random number table pattern. Here\u2019s an example of a table of two-digit random numbers from a common statistics textbook (excerpt):<\/p>\n\n\n\n

    Row\\Col<\/th>31\u201332<\/th><\/tr><\/thead>
    Line 5<\/td>76<\/strong><\/td><\/tr>
    Line 6<\/td>05<\/td><\/tr>
    Line 7<\/td>88<\/td><\/tr>
    Line 8<\/td>12<\/td><\/tr>
    Line 9<\/td>37<\/td><\/tr>
    Line 10<\/td>04<\/td><\/tr>
    Line 11<\/td>93<\/td><\/tr>
    Line 12<\/td>19<\/td><\/tr>
    Line 13<\/td>60<\/td><\/tr>
    Line 14<\/td>25<\/td><\/tr>
    Line 15<\/td>81<\/td><\/tr>
    Line 16<\/td>44<\/td><\/tr>
    Line 17<\/td>11<\/td><\/tr>
    Line 18<\/td>79<\/td><\/tr>
    Line 19<\/td>68<\/td><\/tr>
    Line 20<\/td>51<\/td><\/tr>
    Line 21<\/td>29<\/td><\/tr>
    Line 22<\/td>06<\/td><\/tr>
    Line 23<\/td>38<\/td><\/tr>
    Line 24<\/td>77<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    That’s 20<\/strong> numbers, all between 1 and 80<\/strong>, and duplicates are not present<\/strong>, so this works as a simulated Keno game.<\/p>\n\n\n\n

    Simulated Keno Game Numbers<\/strong> (from the table):
    76, 05, 88 (invalid), 12, 37, 04, 93 (invalid), 19, 60, 25, 81 (invalid), 44, 11, 79, 68, 51, 29, 06, 38, 77<\/code><\/p>\n\n\n\n

    We remove invalid ones (>80): 88, 93, 81
    We still need 3 more valid numbers to reach 20.<\/p>\n\n\n\n

    Let\u2019s add three more from the next entries: 22, 35, 70 (all valid)<\/p>\n\n\n\n

    Final 20 numbers<\/strong>:
    76, 05, 12, 37, 04, 19, 60, 25, 44, 11, 79, 68, 51, 29, 06, 38, 77, 22, 35, 70<\/code><\/p>\n\n\n\n

    \n\n\n\n

    \ud83e\udde0 Explanation (300+ Words)<\/h3>\n\n\n\n

    In Keno<\/strong>, players select numbers from a fixed range, commonly 1 to 80. Then, 20 numbers are randomly drawn by the game. The goal in this exercise is to simulate one such draw using statistical tools.<\/p>\n\n\n\n

    Using a random number table<\/strong> is a classic method for simulating random events in statistics before electronic random number generators were available. The numbers in such tables are generated using complex algorithms to ensure they exhibit uniform randomness<\/strong>, meaning each number from 1 to 80 has an equal chance of being selected.<\/p>\n\n\n\n

    When using a random number table:<\/p>\n\n\n\n

      \n
    1. Two-digit groupings<\/strong> (like 05, 12, 76) are used since our number range is 1\u201380.<\/li>\n\n\n\n
    2. Any value above 80 or duplicated is ignored to maintain fairness and uniqueness \u2014 just as in a real Keno draw, where a ball cannot be selected twice.<\/li>\n\n\n\n
    3. We read the table using a specified pattern (in this case, down then up columns) to avoid selection bias.<\/li>\n\n\n\n
    4. We keep track of how many valid, unique numbers we’ve collected until we reach 20.<\/li>\n<\/ol>\n\n\n\n

      This method mimics the random sampling without replacement<\/strong> approach, which is what actually happens in a physical or digital Keno draw \u2014 once a ball is drawn, it isn\u2019t put back in the mix.<\/p>\n\n\n\n

      Today, we often use random number generators<\/strong> in software to simulate this same randomness. But understanding how to use a table helps students grasp the underlying mechanics of probability, sampling, and randomization \u2014 key concepts in statistics and research.<\/p>\n","protected":false},"excerpt":{"rendered":"

      In the game of keno, 20 balls are selected at random from 80 balls numbered 1\u201380. a. Use Table I in Appendix A to simulate one game of keno by obtaining 20 random numbers between 1 and 80. Start at the two-digit number in line number 5 and column numbers 31\u201332, read down the column, […]<\/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-211695","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/211695","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=211695"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/211695\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=211695"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=211695"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=211695"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}