Elementary Statistics: A Step-by-Step Approach with Formula Card 9th Edition

Published by McGraw-Hill Education
ISBN 10: 0078136334
ISBN 13: 978-0-07813-633-7

Chapter 14 - Sampling and Simulation - 14-1 Common Sampling Techniques - Exercises 14-1 - Page 752: 6

Answer

$Each\:digit\:\left(0-9\right)\:has\:an\:equal\:probability\:of\:occurring\:on\:average,$ $\:though\:not\:necessarily\:in\:every\:sequence.\:Over\:many\:sequences,\:each\:$ $digit\:should\:appear\:roughly\:once\:in\:every\:10\:digits.$

Work Step by Step

$The\:theory\:behind\:random\:numbers\:is\:that\:each\:digit,\:0\:through\:9,\:$ $has\:an\:equal\:probability\:of\:occurring.\:This\:does\:not\:mean\:that\:in\:$ $every\:sequence\:of\:10\:digits\:has\:a\:\frac{1}{10}\:probability.\:This\:does\:not\:mean\:$ $that\:in\:every\:sequence\:of\:10\:digits,\:you\:will\:find\:each\:10\:digit.\:Rather,\:it\:$ $means\:that\:on\:the\:average,\:each\:digit\:will\:occur\:once.\:For\:example,\:$ $the\:digit\:2\:may\:occur\:3\:times\:in\:a\:sequence\:of\:10\:digits.\:But\:in\:later\:$ $sequences,\:it\:may\:not\:occur\:at\:all\:and\:thus\:averaging\:to\:be\:a\:probability\:$ $of\:\frac{1}{10}.$
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