A number in the set $\{50, 51, 52, 53, ... , 999\}$ is randomly selected. What is the probability that it is a two-digit number? Express your answer as a common fraction.
The set $\{50, 51, 52, 53, ... , 999\}$ contains all the numbers from 50 to 999, inclusive. To find the total number of elements in this set, I can subtract the first term from the last term and add one, since the set is arithmetic with a common difference of one. So, the total number of elements is $999 - 50 + 1 = 950$. The two-digit numbers in this set are the ones from 50 to 99, inclusive. To find the number of two-digit numbers in this set, I can use the same formula as before: $99 - 50 + 1 = 50$. The probability of randomly selecting a two-digit number from this set is the ratio of the number of two-digit numbers to the total number of elements. So, the probability is $\frac{50}{950} = \frac{1}{19}$. 