SOLUTION: A security specialist is disigning a code for a security system, The code will use only the letters A, B, C. If the specialist wants the probability of guessing the code at randome

Question 1138065: A security specialist is disigning a code for a security system, The code will use only the letters A, B, C. If the specialist wants the probability of guessing the code at randometo be less than 0.001, how long must the code be?
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the answer must be 7 ???
Answer by ikleyn(52779) (Show Source): You can put this solution on YOUR website!
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When you use the words, consisting of three letters A,B and C (uppercase) of the length "n"  (n symbols), 


then the number of all possible codes is .


In order for the probability to guess a password randomly be less  than 0.001, you need to have more than 1000 such codes (passwords).


It gives you inequality


      > 1000.


Its solution is


     n*log(3) > log(1000) = 3,   or


     n >  = 6.28.


Since n must be integer, it gives you inequality n >= 7 as your ANSWER.

Solved, explained and completed.

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