document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192270>Question 1192270</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The communication channel transmits a three-digit number M = 873, written in decimal digits. Each digit is passed correctly with probability 0.62 and is converted to any other digit with probability (1 - 0.62) / 9. <BR>\n" );
document.write( "a) what is the probability that transmitting the number M will decrease it?<BR>\n" );
document.write( "b) what is the maximum increase in the probability of a decrease in the number when adding a digit from the right? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #824176 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52835)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=824176\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "The communication channel transmits a three-digit number M = 873, written in decimal digits. <BR>\n" );
document.write( "Each digit is passed correctly with probability 0.62 and is converted to any other digit <BR>\n" );
document.write( "with probability (1 - 0.62) / 9.<BR>\n" );
document.write( "a) what is the probability that transmitting the number M will decrease it?<BR>\n" );
document.write( "b) what is the maximum increase in the probability of a decrease in the number when adding a digit from the right?<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I will solve part &nbsp;(a), &nbsp;only.\r<BR>\n" );
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document.write( "The probability that transmitting the number M= 873 will increase it is this sum\r\n" );
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document.write( "    P =   P(first digit 8 is no change)*P(second digit 7 is no change)*P(third digit 3 increases) +\r\n" );
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document.write( "        + P(first digit 8 is no change)*P(second digit 7 increases) +\r\n" );
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document.write( "        + P(first digit 8 is increases)  = \r\n" );
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document.write( "        = 0.62*0.62*(6*((1-0.62)/9)) + 0.62*(2*((1-0.62)/9)) + 1*((1-0.62)/9) = 0.191959  (rounded).    <U>ANSWER</U>\r\n" );
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document.write( "It requires some comments.\r\n" );
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document.write( "P(third digit 3 increases) = 6*((1-0.62)/9),  since there are 6 possibilities to increase 3: they are 4,5,6,7,8,9.\r\n" );
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document.write( "P(second digit 7 increases) = 2*((1-0.62)/9), since there are 2 possibilities to increase 7: they are 8,9.\r\n" );
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document.write( "P(first digit 8 is increases) = 1*((1-0.62)/9), since there is only 1 possibility to increase 8: it is 9.\r\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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