document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193822>Question 1193822</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A fair decimal die is rolled three times. What is the probability that\r<BR>\n" );
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document.write( "All three outcomes represent odd numbers?<BR>\n" );
document.write( "Answer:  1/8\r<BR>\n" );
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document.write( "The digit 1 occurs at least once?<BR>\n" );
document.write( "Answer:  22/125 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825858 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825858\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Problem 1\r<BR>\n" );
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document.write( "I'm assuming a decimal die consists of the ten numbers 1,2,3,4,5,6,7,8,9,10<BR>\n" );
document.write( "Though if instead it's 0,1,2,3,4,5,6,7,8,9, then the steps and answers mentioned below would be practically identical.\r<BR>\n" );
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document.write( "Half of them are odd (1,3,5,7,9) which means 1/2 is the probability of getting an odd result when rolling the die.\r<BR>\n" );
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document.write( "The probability of getting three odd numbers in a row is (1/2)*(1/2)*(1/2) = (1/2)^3 = 1/8<BR>\n" );
document.write( "Each roll is independent of one another.\r<BR>\n" );
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document.write( "<font color=red>Answer: 1/8</font><BR>\n" );
document.write( "You have the correct answer. Nice work.\r<BR>\n" );
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document.write( "Problem 2\r<BR>\n" );
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document.write( "Here's the sample space<BR>\n" );
document.write( "{1,2,3,4,5,6,7,8,9,10}<BR>\n" );
document.write( "which is the set of all possible outcomes.\r<BR>\n" );
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document.write( "Ask yourself: what is the probability of rolling anything but \"1\"? <BR>\n" );
document.write( "The answer would be 9/10 since we have nine things we want (2 through 10) out of 10 outcomes total.<BR>\n" );
document.write( "Stringing three such results together in a row would have the odds of (9/10)^3 = 729/1000<BR>\n" );
document.write( "This represents the probability of rolling three items in a row, none of which are \"1\". Repeats are allowed.\r<BR>\n" );
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document.write( "The complement of this probability is<BR>\n" );
document.write( "1 - (729/1000) = 271/1000<BR>\n" );
document.write( "which represents the probability of the result \"1\" showing up at least once. This is because we have two options of either: 1 shows up at least once, or 1 doesn't show up at all.\r<BR>\n" );
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document.write( "<font color=red>Answer: 271/1000</font><BR>\n" );
document.write( "I'm not sure how you got 22/125, so please let me know your steps and/or thought process. If your teacher wrote 22/125 as the answer, then s/he made a typo. If I made a mistake somewhere, then please let me know. <BR>\n" );
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