A thief steals an ATM card and must randomly guess the correct three-digit pin code from a 9-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?

The thief has a 0.11% probability of hitting the pin code on the first try.

Explanation:

Simply, if the ATM card has a 3-digit code that can be repeated, and the board has 9 numbers (for example, from 1 to 9), we must start from the smallest number that could be formed with these numbers to the highest number that these numbers could also compose, which in the case would be 111 and 999. Then, 889 different numbers could be formed (it is the distance between 111 and 999), with which the possibility of hitting the key to the first attempt would be 1 in 889 times, or 1/889.

To take the probability to a percentage, we must know that 889 / 8.89 gives 100. Therefore, dividing 1 / 8.89 we will know the percentage of probabilities of hitting the key on the first attempt: 1 / 8.89 = 0.11.

This shows us that the thief has a 0.11% probability of hitting the key on the first try.