Considering that it is allowed to repeat the digits in the three-digit code, we have,
10 x 10 x 10 ways
which is equal to 1000 ways.
For the scenario that only even numbers without repetition can be included, we have,
5 x 3 x 1 ways
which is equal to 15 ways.
The probability is therefore 15/1000 or 3/200.