A spyware is trying to break into a system by guessing its p

A spyware is trying to break into a system by guessing its password. It does not give up until it tries 1 million dierent passwords. What is the probability that it will guess the password and break in if by rules, the password must consist of

(a) 6 dierent lower-case letters

(b) 6 dierent letters, some may be upper-case, and it is case-sensitive

(c) any 6 letters, upper- or lower-case, and it is case-sensitive

(d) any 6 characters including letters and digits

Solution

a)

There are 26P6 = 26!/20! such passwords.

Hence,

P = 1000000/(26P6) = 0.006032615 [ANSWER]

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b)

There are 52P6 = 52!/46! such passwords (26 lowercase + 26 uppercase = 52 characters).

Hence,

P = 1000000/(52P6) = 6.82215*10^-5 [ANSWER]

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c)

There are 52^6 such passwords.

Hence,

P = 1000000/(52^6) = 5.05801*10^-5 [ANSWER]

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d)

THere are 62^6 such passwords (26 lowercase + 26 uppercase + 10 digits = 62 characters).

Hence,

P = 1000000/(62^6) = 1.76056*10^-5 [ANSWER]