macattack wrote:Just for fun.. what you are saying suggests that P(x>=y)=P(x>y) but knowing that the number of desired outcome of the former in definitely higher than the latter definitely weakens that argument.
You're right in that we are adding a LOT of desired outcomes. In fact, we are adding an infinite number of outcomes.
Since we're adding the points on the line segment, it appears that the probability should increase. By how much does it increase?
Well, let's find P(the point is on the line segment in region R)
Since there is an infinite number of points on the line segment, and since region R consists of an infinite number of points, it appears that P(the point is on the line segment in region R) = infinite/infinite.
At this point, I believe we're getting into something called "countably infinite" (although it may also be called something else).
Although I can't answer your question, I can assure you that you don't need to worry about things like the area of a line.
What you do need to know is that, when it comes to probabilities involving area, the probability of an event proportional to the target area.
Cheers,
Brent
