eli5 what is the difference between probability and probability density.

Question

I’ve read several posts and can’t put my finger on the exact difference. Is there an easier example someone could give me to grasp this concept.

In: 5

Answer 1

Probability is the chance that one event happens.

Probability density is the infinitesemal chance that an infinitesemal event happens. That means, the event is very unlikely because its very specific.

For example the chance that the temperature measured is exactly 20.00..°C with infinte zeros after the decimal point is pretty much zero.

So giving a probability makes no sense. We give it a probability density of Chance per degree range. For example 5%/°C . If you integrate over that between certain limits you can calculate a probability again, for example 19°C-21°C has a probability of 10%. And 19.9°C-20.1°C would be 1% (for a constant probability density of 5%/°C)