One day, Larry writes down the numbers 1, 2, ..., 999. Larry chooses one of the digits written down at random. What is the probability that Larry chooses a 7?

The probability that Larry chooses a 7 is 28/297.

There are a total of 2889 digits between 1 and 999.

There are exactly 300 "7s" between 1 and 999, including duplicates such as: 77, 777........etc.

Then the probability is:300 / 2889 = ~0.10384 x 100 =10.384%.