If the digets repeat what is the probability that a randomly chosen combination will have all the same digits?

Question

the combination for a locker consists of 3 1-digit numbers. also what if they can repeat

Answer 1

10/1000 or 1/100 - if 0 can be used

9/999 or 1/111 if 0 can not be used.

Answer 2

The first digit can be anything.

The second digit has a 1/10 chance of matching.

The third digit has a 1/10 chance of matching.

Probability(all digits the same) = 1 x 1/10 x 1/10 = 1/100

Answer:

1/100 = 0.01 = 1%

Another way to think of this.  There are 10 combinations with all digits the same (000, 111, 222, 333, 444, 555, 666, 777, 888, 999).

There are 10 choices for the first digit, 10 choices for the second digit and 10 choices for the third digit.  Thus there are 10 x 10 x 10 = 1000 ways to form a combination.

The probability of getting all digits the same is the ways to get them the same (10) divided by the total number of combinations (1000).

Answer:

10/1000 = 1/100 = 0.01 = 1%