A thief steals an ATM card and must randomly guess the correct three-digit pin code from a 10-key keypad. Repetition of digits is allowed The number of possible codes is 1000 . (Type an integer or fraction. Simplify your answer.) The probability that the correct code is given on the first try is (Type an integer or fraction. Simplify your answer.)

The total number of possible three-digit PIN combinations, as you noted, is 1000 (ranging from 000 to 999). Since the thief makes a guess and there is only one correct code out of these 1000 possibilities, the chances of guessing it correctly on the first try are 1 in 1000. Hence, the probability of the correct code being entered on the first attempt is \( \frac{1}{1000} \). This scenario really highlights the importance of using strong, complex PINs or passwords. Rather than sticking to easily memorable numbers like ‘123’ or years like ‘1990,’ consider using phrases or combinations that are less predictable. Adding letters, special characters, and even changing the order of those digits can significantly enhance security, making it much tougher for potential intruders to break in. It's like giving your PIN a superhero cape!