3. A credit card contains 16 digits. Is also contains the month and year of expi

Question

3. A credit card contains 16 digits. Is also contains the month and year of expiration. Suppose there are 2 million credit card holders with random unique card numbers. A hacker randomly selects a 16-digit credit card number (a) What is the probability that it belongs to a user? (3 pts) (b) The hacker (inclusive). What is the probability that the hacker can guess the expiration year and month? (3 pts) (c) What is the probability that the hacker can guess the credit card number, expiration year, and expiration month? (2 pts)

Explanation / Answer

Answer to the question is as follows. Please don't hesitate to write back to me in case of doubts:

a.

The number of combos of a 16-digit CC number is ?

Each of the digits can hold 0 to 9 or 10 numbers.

So, 10^16 combinations in total, Out of that 2*10^6 are allocated

Hence, P(it belongs to user) = 2*10^6/10^16 = 2/10^10 = 5*10^-9

b. So, 2018-2025 is 8 years. And any of the 12 months are to be guessed.

So, P( getting month and year right) = 1/8 * 1/12 = 1/96

c. P( getting month , year and CC number right) = 1/96* 5*10^-9 = 5.2*10^-11

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