document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200499>Question 1200499</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 4 digits long, and that each digit could be a number between 0 and 5. Assume that the hacker makes random guesses.<BR>\n" );
document.write( "What is the probability that the hacker guesses the password on his first try? Please report the answer to four decimal places.<BR>\n" );
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document.write( "Answer: <font color=red>0.0008</font>\r<BR>\n" );
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document.write( "Reason:\r<BR>\n" );
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document.write( "A = 1 = number of correct passwords<BR>\n" );
document.write( "B = 6*6*6*6 = 6^4 = 1296 = number of possible 4-digit passwords such that each digit is between 0 and 5 (there are 5-0+1 = 6 choices per digit)<BR>\n" );
document.write( "Repeated digits are allowed.\r<BR>\n" );
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document.write( "A/B = 1/1296 <BR>\n" );
document.write( "A/B = 0.00077160493828<BR>\n" );
document.write( "A/B = <font color=red>0.0008</font> is the approximate probability they correctly guess the password on the first try if guessing at random.<BR>\n" );
document.write( "This is about a 0.08% chance.<BR>\n" );
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