Question

A computer system uses passwords that are exactly 8 characters and each character is one of the 26 lowercase letters (a-z), uppercase letters (A-Z), or 10 integers (0-9). Let A denote the subset of possible passwords that do not begin with a vowel (a, e, i, o, u, A, E, I, O, U) and B denote the subset of possible passwords that do not end with a number (0-9).(a)What is the probability that a hacker randomly selects a password that matches your password?(b)Suppose a hacker knows that your password is in event A and selects a password at random from this subset. What is the probability that it matches your password?(c)Suppose a hacker knows that your password is in event A and B and selects a password at random from this subset. What is the probability that it matches your password?

Answer 1

Answer:

a) 1 in 218 trillion

b) 1 in 183 trillion

c) 1 in 153 trillion

Step-by-step explanation:

Total number of character 26 upper case + 26 lower case + 10 numbers = 62 characters

a) the total possible combination of password is = 62*62*62*62*62*62*62*62= 218,340,105,584,896 combination

218 trillion combination = 1 in 218 trillion

b) number of exempted character 10.... 62-10=52

total possible password combination 52*62*62*62*62*62*62*62= 183,123,959522,816 = 183 trillion possible combination

Probability of selecting a password from this subset is 1 in 183 trillion

Number of character exempted 10 in the beginning and 10 in the end

Total possible password combination is

52*62*62*62*62*62*62*52= 153,587,837,019,136= 153 trillion possible combination probability of picking the right password is 1 in 153 trillion