Question

Two new computer codes are being developed to prevent unauthorized
access to classified information. The first consists of six digits (each chosen
from 0 to 9); the second consists of three digits (from 0 to 9) followed by two
letters (A to Z, excluding I and O).

(i) If both codes are implemented, the first followed by the second, what is
probability of gaining access in a single attempt?

Answer 1

If repeating is allowed than you can generate $10^6$ passwords of length $6$ with $10$ digits.

If repeating is allowed than you can generate $10^3\cdot(26-2)^2$  passwords of length $3+2.$

If both codes are implemented, the first followed by the second you can generate $10^6\cdot10^3\cdot(26-2)^2=5.76\cdot10^{11}$ passwords.

Hence probability of gaining access in a single attempt is

$$p=\dfrac{1}{5.76\cdot10^{11}}=1.736\times10^{-12}$$