Neco 2024 Data Processing Question 31

A company uses a two‑factor authentication system. The probability that a random attacker guesses a user's password in a single attempt is \(\frac{1}{8000}\). The probability that the attacker can bypass the hardware token in a single attempt is \(\frac{1}{400}\). Each employee makes 100 login attempts per year and the company has 2000 employees. (a) Assuming the two events are independent, compute the expected number of accounts that would be compromised in a year. (b) The security policy requires the expected number of compromised accounts to be less than 1. If the company can only improve one of the two probabilities and chooses to halve it, which probability should be halved to meet the requirement? State the new expected number after the improvement.