Question

Suppose a computer's login mechanism first asks for a user name, and then for the password, regardless of whether or not the login name is that of a valid user. Herman the Hacker has a list of 10,000 commonly used login names, and a list of 100,000 commonly used passwords. On this computer, there are 100 accounts that have both a login name on the first list and a password on the second list. For simplicity, assume that no other accounts have either a login name or password on these lists.
Herman has written code that can attempt 1000 logins per second on this computer. This program repeatedly chooses a random login name from the first list and a random password from the second list. Compute the expected number of seconds it will take Herman to break into some account on the machine, and identify that number from the list below.
Hint: Since names and passwords are chosen randomly, repetitions are possible. It may indeed be easier to forget what names/passwords have been tried than to keep a list of what has been tried and avoid duplicate attempts. As a result, there is an easy formula for the expected number of tries. If the probability of success on any given try is p, then the expected number of tries until the first success is exactly 1/p.
A. 1.1
B. 100.1
C. 10,000
D. 1000.1

Answer 1

The expected number of seconds it will take Herman to break into  (or hack) some account on the machine is 1.1 seconds. (Option A) See the explanation below.

What does it mean to hack a machine?

The act of subverting digital systems and networks by gaining unauthorized access to a computer system or account is a popular definition of hacking.

Although hacking is not always harmful, it is most frequently linked to online crime and data theft by cybercriminals.

What is the explanation for the above answer?

With 10,000 login names available, we can assume that 100 of them are accurate, as the question suggests.

The likelihood of receiving the proper login name is therefore

P 1 = 100 10,000

P1 = 0.01

In the same vein, among 100,000 password we can assume that only 100 are correct, therefore, the probability of getting the right password is.

P 2 = 100 ÷ 100,000

P2 = 0.001

That that where the probability of success on any given try is p, then the expected number of tries until the first success is exactly 1 ÷ P.

Therefore, the expected number of trials before the first successful login name is = 1÷ P1​​​​​1

= 1 ÷ 0.01

= 100

The above also works for the password:
1÷ P2

= 1 ÷ 0.001

=1000

Therefore, it will take 100+ 1000 = 1100 attempts to finally get the initial login name and password.

Given that Henrietta created programming that allows this computer to try 1000 logins every second.

Therefore, 1100 x 1000 sec = 1.1 sec is the anticipated time it will take Henrietta to gain access to a machine account.

Learn more about hacking at;
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Answer 2

The  expected number of seconds that will take to Herman to break into some account on the machine is 10.000. So Letter C.

Firstly, the probability of finding a correct login name (100) out of first list (1000) = 100/1000 = 1/100.

Second, After finding a login name, exactly one password will correspond to the found login name. As both the events are independent, hence:

Probability(p) = 1/100 x 1/100000 = 1/10000000.

Therefore, expected numbers of tries = 1/p = 10000000.

The code can attempt 1000 tries per second. So the expected numbers os seconds that will take to Herman break into some account will be:

10000000/1000 = 10.000.

See more about probability at: brainly.com/question/16259980

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