Candice wants to randomly generate a 4-digit personal identification number, or PIN, for her bank card. Calculate the theoretical probability of all four numbers being the same.
To calculate the theoretical probability of all four numbers being the same in a 4-digit PIN, we need to consider the total number of possible 4-digit PINs and the number of PINs where all four numbers are the same.
There are 10 possible digits (0-9) that can be used for each of the four positions in the PIN. Since all four numbers must be the same, there is only one possible combination for the PIN.
So, the number of PINs where all four numbers are the same is 1.
The total number of possible 4-digit PINs is 10^4 = 10,000.
Therefore, the theoretical probability of all four numbers being the same in a randomly generated 4-digit PIN is:
1 / 10,000 = 0.0001 = 0.01%