Answer to Question #234527 in Statistics and Probability for Teddy

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

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