Answer
See the detailed answer below.
Work Step by Step
The easiest way to understand the difference between probability and probability density is by comparing it to mass and mass density.
Think of mass as how much stuff is in something, like how heavy an object is. Mass density is how packed that stuff is in a specific space. For example, if you have a box full of sand and a box full of air, the sand has more mass density because it’s heavier and packed more tightly in the same space.
Probability is like predicting the chance of something happening. The result is always a number between 0 and 1. If it’s definitely going to happen, the probability is 1, and if it’s impossible to happen, then the probability is 0.
Probability density, on the other hand, is like a guide that shows where something is more or less likely to occur. Imagine dropping a ball into a bowl, the ball is more likely to end up at the bottom because that’s the most probable spot.
In the same way that mass density helps you figure out where the most mass is, probability density helps you figure out where things are most likely to happen. Both depend on the size of the area you’re focused on.
From all the above,
$\rm \underline{Probability}$ is a numerical measure of the likelihood of an event occurring. It ranges from 0 to 1, where 0 indicates impossibility and 1 indicates certainty.
$\rm \underline{Probability \; density}$ is a mathematical function that represents the probability distribution of a continuous random variable. It is not directly the probability of a specific value, but rather the probability of the variable falling within a certain range.
