What exactly is the difference bet. a CDF and a PDF?

[Peon666]

Homework Statement

I understand that PDF is a derivative of CDF and hence CDF is the integral of PDF. But I don't understand the difference between PDF and simply probability? What exactly is the differece? What extra things does PDF tell us which simple probability does not?

Homework Equations

For example, we toss a coin and a head comes. Probability of it is 1/2. What's PDF in this case?

The Attempt at a Solution

 

[rock.freak667]

Well say you toss a coin 1000 times and you want the probability of exactly 3 heads. To write down all the possibilities, would take a long time. The pdf is basically a single formula that would describe the probabilities. So for the coin toss (it follows a binomial distribution)
P(X=3)= ¹⁰⁰⁰C₃(1/2)³(1/2)^1000-3

A cdf sums the probabilities.


EDIT: that is for a discrete distribution

 

[Peon666]

I think I'm getting to the idea but I'm not completely clear yet. I understand the difference between CDF and PDF but what's the difference between simple probability and PDF?

And do we always follow the binomial distribution in PDF?