If the discrete random variable $x$ is uniformly distributed over the integers from $10$ to $20$ inclusive, what is the probability that $x$ equals $15$?

• A. $\frac{1}{20}$
• B. $\frac{1}{11}$
• C. $\frac{1}{15}$
• D. $\frac{1}{10}$

Answer: (B)

Verified step by step guidance

1. Identify the range of the discrete uniform distribution. Here, the random variable \( x \) takes integer values from 10 to 20 inclusive.
2. Calculate the total number of possible outcomes. Since the values are from 10 to 20 inclusive, the number of outcomes is \( 20 - 10 + 1 \).
3. Recall that for a discrete uniform distribution, the probability of each outcome is equal and given by \( \frac{1}{\text{number of outcomes}} \).
4. Substitute the number of outcomes into the formula to find the probability that \( x = 15 \).
5. Express the probability as a simplified fraction \( \frac{1}{\text{number of outcomes}} \), which represents the probability that \( x \) equals 15.