Let $D$ be the number of students living in dormitories.
We are given that 10% of students live in dormitories, so $D = 0.10N$.
A random sample of 100 students is selected. We want to find the probability that a student selected from the dormitory is in this sample.
Let $X$ be the number of students in the sample who live in dormitories.
Then $X$ follows a hypergeometric distribution with parameters $N$, $D$, and $n=100$.
The probability of selecting a student from the dormitory is the ratio of the number of students in dormitories to the total number of students: $\frac{D}{N} = 0.10$.
The probability that a randomly selected student lives in a dormitory is 0.10. The probability that a student from the sample of 100 lives in a dormitory is also 0.10, assuming the sample is a simple random sample. The probability doesn't change based on the sample size.
The probability that at least one student from the dormitory is selected in the sample of 100 is given by:
$P(X \ge 1) = 1 - P(X=0) = 1 - \frac{\binom{N-D}{100} \binom{D}{0}}{\binom{N}{100}} = 1 - \frac{\binom{0.9N}{100}}{\binom{N}{100}}$
For large N, the hypergeometric distribution can be approximated by a binomial distribution with parameters $n=100$ and $p=0.10$.
The probability of selecting a student from the dormitory is approximately $0.10$. The expected number of students from the dormitory in the sample is $100 \times 0.10 = 10$.
The probability that a randomly selected student from the sample of 100 is from a dormitory is approximately 0.10.
Final Answer: The final answer is $\boxed{0.1}$