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) Which code is better at preventing unauthorized access (defined as break
ing the code in one attempt)?

Answer 1

(i) Code1: It has 6 digits chosen from 0 to 9. So the total available combinations are $10^6$ . In one attempt a person can only try one combination, so the probability that this combination is the correct code is $\frac{1}{10^6} = 10^{-6}$

Code 2: The second code has 3 digits taken from 0 to 9, and 2 letters taken from 24 alphabets (Since I and O are excluded). So total available combinations are $10^3$ multiplied by 242. So 576,000 combinations. In one attempt a person can only try one combination, so the probability that this combination is the correct code is $\frac{1}{576000}$ which is equal to $1.736 \times 10^{-6}$

Since the probability for breaking the code in one try is more for code2, Code1 is the better code for preventing unauthorized access.