document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=468417>Question 468417</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I cannot for the life of me figure this one out, I have tried several time and still come up with the wrong answer.  The questions is:<BR>\n" );
document.write( "The access code for a garage door consists of three digits. Each digit can be 2 through 7 and each digit can be repeated.<BR>\n" );
document.write( "a)Find the number of possible access codes<BR>\n" );
document.write( "b)What is the probability of randomly selecting the correct access code?<BR>\n" );
document.write( "c)What is the probability of not selecting the correct access code?\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #321409 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=321409\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there are 6 digits from 2 through 7.<BR>\n" );
document.write( "they are:   {2,3,4,5,6,7}<BR>\n" );
document.write( "The number of possible access codes are 6^3 = 216<BR>\n" );
document.write( "The probability of randomly selecting the correct access code is (1/6)^3 = 1/216.<BR>\n" );
document.write( "The probability of not selecting the correct code is 1 - 1/216 = 215/216.<BR>\n" );
document.write( "I can't show you all the codes because there are too many.<BR>\n" );
document.write( "I can, however, show you a much simpler situation.<BR>\n" );
document.write( "suppose the possible digits are 3 and 4.<BR>\n" );
document.write( "That's 2 possible selections per digit.<BR>\n" );
document.write( "With repetition of digits, the number of possible combinations are 2^3 = 8<BR>\n" );
document.write( "Those possible combinations are:<BR>\n" );
document.write( "111<BR>\n" );
document.write( "112<BR>\n" );
document.write( "121<BR>\n" );
document.write( "122<BR>\n" );
document.write( "211<BR>\n" );
document.write( "212<BR>\n" );
document.write( "221<BR>\n" );
document.write( "222<BR>\n" );
document.write( "The probability of randomly selecting the correct code is (1/2)^2 which becomes 1/8.<BR>\n" );
document.write( "Assume the code is 211.<BR>\n" );
document.write( "You can see that there is only 1 code out of the 8 possible codes that contains 211.<BR>\n" );
document.write( "The probability of selecting 211 randomly is therefore 1 out of 8.<BR>\n" );
document.write( "The probability of NOT selecting the correct code is 1 - 1/8 = 7/8.<BR>\n" );
document.write( "You can see that there are 7 out of 8 codes that do not contain 211.<BR>\n" );
document.write( "With 6 possible numbers per digit, the number of possibilities is much greater and the probability of guessing the correct code is also much smaller.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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