What does it mean for points to be picked uniformly and independently? I saw a which said that points were picked uniformly and independently. I have a feeling this is important for the solution but I am not sure what they mean by uniformly and independently. Any help would be appreciated. I will post the original question here.
Question:
Four points are chosen uniformly and independently at random in the interior of a given circle. Find the probability that they are the vertices of a convex quadrilateral.
Note: I am not looking for a solution to the problem, just for clarification on what uniformly and independently mean.

I'm reformulating an earlier comment I made as an answer.
"Uniformly" means without applying any preference to a particular part of a region. So, if you were choosing uniformly amongst a discrete set of options, say the numbers $1$ through $10$, you're just as likely to choose $5$ as you are $2$: the probability of drawing any given number is $1$ in $10$. 
"Independently" here really just means that the last point you chose has no impact on any future point you choose. So, say that $A1$ is your first choice and $A2$ your second choice. The probability of drawing both is $\Pr[A1 \cap A2]= \Pr[A1] \cdot \Pr[A2]$.
