Question

A hard-headed hacker is attempting to login into Larry’s Amazon account by guessing his password. The hacker does not give up until she tries 1 thousand different passwords. What is the probability that she will guess the password and break in if by rules, the password must consist of:

a. 8 different lower-case letters

b. 8 different letters, some may be upper-case, and it is case sensitive

c. any 8 letters, upper- or lower-case, and it is case sensitive

d. any 8 characters including letters and digits

Answer 1

Answer:

Given that:

A hard-headed hacker is attempting to login into Larry’s Amazon account by guessing his password. The hacker does not give up until she tries 1 thousand different passwords.

a) 8 different lower-case letters

number of ways to create 8 different lower -case letters password =²⁶P₈ =62990928000

hence probability that she will guess the password =1000/62990928000 =

b)  8 different letters, some may be upper-case, and it is case sensitive

number of ways to create 8 different letters, some may be upper-case, and it is case sensitive =⁵²P₈

hence probability that she will guess the password =1000/⁵²P₈ =

c) any 8 letters, upper- or lower-case, and it is case sensitive

number of ways =

probability =  

d) any 8 characters including letters and digits

Here as number of digits are 10 ; therefore options for each character =26 lower case+26 upper case+10 digits =62

number of ways =

probability =