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

Question

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 can reasonably guess the year of expiration is a number between 2018-2025 (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?

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 can reasonably guess the year of expiration is a number between 2018-2025 (incusive). What is the probability that the hacker can guess the expiration year and month? (3 pts) 3 PtSts (c) What is the probability that the hacker can guess the credit card number, expiration year, and expiration month? (2 pts)

Explanation / Answer

(a)

A credit card contains 16 digits. So, the possible numbers of credit cards is 1016

Number of credit card holders = 2 million = 2 x 106

So, the probability that it belongs to a user = Number of credit card holders / Possible numbers of credit cards

=  2 x 106 / 1016

= 2 x 10-10

(b)

Possible number of expiration years = 8

Possible number of expiration months = 12

Possible number of combination of expiration year and month = 8 * 12 = 96

The probability that the hacker can guess the expiration year and month = 1 / 96

(c)

The probability that the hacker can guess the credit card number, expiration year, and expiration month

=  2 x 10-10 * (1/96)

= 0.0208 x 10-10

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