A credit card contains 16 digits. It also contains a monthand year of expiration

Question

A credit card contains 16 digits. It also contains a monthand year of expiration. Suppose there are one million usersof a credit card with unique card numbers. A hacker randomlyselects a 16 digit credit card number. (a) What is the probability that it belongs to a user? (b) Suppose a hacker has a 25% chance of correctly guessingthe year your card expires and randomly selects one of the 12months. What is the probability that the hacker correctlyselects the month and year of expiration? (a) What is the probability that it belongs to a user? (b) Suppose a hacker has a 25% chance of correctly guessingthe year your card expires and randomly selects one of the 12months. What is the probability that the hacker correctlyselects the month and year of expiration?

Explanation / Answer

Assuming that the 16 digit field is all numeric and that anydigit 0-9 can be used in any of the 16 positions... a) There are 1016 possible card numbers. If amillion cards have been issued, the probability that a randomlyselected 16 digit number matches an issued card is1e6/1e16=1/1e10 b) (1/4)(1/12)=1/48 probability of guessing year andmonth.

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