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

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

hence probability that she will guess the password =1000/62990928000 =1.59*10^-8

b)

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 =3.30*10^-11

c)

number of ways =52⁸

probability =1000/52⁸ =1.87*10^-11

d)here as number of digits are 10 ; therefore options for each chracter =26 lower case+26 upper case+10 digits =62

number of ways =62⁸

probability =1000/62⁸ =4.58*10^-12