---
title: "relative probability"
type: concept
source: https://www.jemoka.com/posts/kbhrelative_probability/
confidence: high
status: active
---

Let \(X \sim \mathcal{N}\).
&ldquo;How much more likely is \(x=10\) than \(x=5\)?&rdquo;
We note that \(P(x=value) = 0\) for any value if \(X\) is continuous. However, we can still get an answer:
\begin{equation} \frac{\dd{X} P(x=10)}{\dd{X} P(x=5)} \end{equation}
these two things cancel out. Therefore, you can just divide the PDF:
\begin{equation} \frac{f(x=10)}{f(x=5)} \end{equation}
