Problem 2 A credit card contains 16 digits It also contains

Problem #2: A credit card contains 16 digits. It also contains the month and year of expiration. Suppose there are 1 million credit card holders with unique card numbers are valid. A hacker randomly selects a 16-digit credit card number. a) what is the probability that it is a invalid number? b) What is the probability that it belongs to a user? c) Suppose a hacker has a 10% chance of correctly guessing the year your card expires and randomly selects 1 of the 12 months. What is the probability that the hacker correctly selects the month and year of expiration?

Solution

(a)

Total number of possible 16 digit numbers = 10^16

P(Number is valid) = 10^6/10^16 = 1/10^10

Therefore,

P(Number is invalid) = 1 - 1/10^10 = 0.9999999999 Answer

(b)

P(It belongs to a user) = 10^6/10^16 = 1/10^10   Answer

(c)

P(Hacker correctly guesses month and year) = 0.1 * 1/12 = 0.0083 Answer