Answer to Question #231650 in Statistics and Probability for Jamilah

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)?

[3 marks]

(ii) If both codes are implemented, the first followed by the second, what is

probability of gaining access in a single attempt?

Answer 1

(i)Code1: It has 6 digits chosen from 0 to 9. So the total available combinations are 10⁶.

In one attempt a person can only try one combination, so the probability that this combination is the correct code is $1/10^6 = 10^{-6}.$

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 $10^3\cdot 24^2=576000.$

In one attempt a person can only try one combination, so the probability that this combination is the correct code is $1/576000=1.7361\times 10^{-6}.$

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

(ii) If both codes are implemented the first followed by the second, there will be 9 digits and 2 letters in the new code. So the total available combinations are $10^{6+3}\cdot24^2=5.76\cdot 10^{11}.$

In one attempt a person can only try one combination, so the probability that this combination is the correct code is $1/(5.76\cdot10^{11})=1.7361\times 10^{-12}.$ As expected, this is really small when compared to the other two probabilities that we found out because this code is longer and is harder to break.