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## Homework Statement

Consider a simple password scheme using only two lowercase letters. A hacker is given 5 chances to guess the pw before being detected. Computer probability hacker is successful.

## Homework Equations

p = 1/(26*26)

## The Attempt at a Solution

I'm assuming the hacker isn't guessing randomly, but without replacement.

I feel that I may be multiplying the wrong probabilities, but what the heck:

P(attacker is successful) = [tex]\frac{1}{26^{2}} + \frac{1}{26^{2}*(26^{2}-1)} + \frac{1}{26^{2}*(26^{2}-1)*(26^{2}-2)} + \frac{1}{26^{2}*(26^{2}-1)*(26^{2}-2)*(26^{2}-3)} + \frac{1}{26^{2}*(26^{2}-1)*(26^{2}-2)*(26^{2}-3)*(26^{2}-4)}[/tex]

This was an intuitive guess, since each guess is equally likely, I just subtract one from the sample space for each of the five guesses.