document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=387985>Question 387985</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you randomly choose a number between 1 and 100. What are the odds against choosing a prime number?\r<BR>\n" );
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document.write( "Your computer password has 4 capital letters followed by 3 digits. Your friend randomly chooses 4 capital letters and 3 digits. Use a calculator to find the probability that your friend chooses your password.? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #274278 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=274278\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For the first problem you will just have to count the number of prime numbers between 1 and 100. (Remember that 1 is not considered prime or composite.) The probability will be the number of primes over the total number of possible numbers (100).<br><BR>\n" );
document.write( "For the second problem, since it does not say that the 4 letters must be difference we must assume that repetitions are possible. And we must also assume that your friend gets only one guess.<br><BR>\n" );
document.write( "The number of possible passwords would be:<BR>\n" );
document.write( "26*26*26*26*10*10*10<BR>\n" );
document.write( "The probability of your friend guessing your password in one guess:<BR>\n" );
document.write( "1/26*26*26*26*10*10*10<BR>\n" );
document.write( "(Use your calculator to simplify the denominator.) </SPAN>\n" );
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