Why is the probability of "$\le$" the same as "$\lt$"? The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function:
$f(x)= 0.075x+0.2$ for $3\le{x}\le5$
$f(x) = 0$        otherwise.
Calculate $P(X\le4)$ and compare to $P(X\lt4)$.
In my solution, I calculate $P(X\le4)$ and $P(X\lt4)$ by integral and I see that $P(X\le4)=P(X\lt4)$. My questions are:

*

*Are they always equal to each other in every other case?

*Why  can they equal to each other while $P(X=4)\neq0$?

Thanks a lot for your help!

To complement the other answer I want to say that probability is, in some sense, a branch of measure theory. That is, probability is a way to assigns to some subsets "a kind of area", or "length", loosely speaking.
And in measure theory you realize you can have sets which although not being empty they have "length" $0$ (for example $A=\{4\}$ in your case). And this is the reason why you can find non impossible events whose probability is $0$.
