Thread: basic question about probabililty = zero

Suppose one asks what the probability is that a point on a sphere is on the equator? On one side, that would be zero, since the equator has measure zero on the sphere. On the other side, probability zero means that it is impossible, which it clearly isn't. What is the usual solution to this?

Originally Posted by nomadreid

On the other side, probability zero means that it is impossible,

That is not true, choose for example the probability space with and defined by .

Originally Posted by nomadreid

Suppose one asks what the probability is that a point on a sphere is on the equator? On one side, that would be zero, since the equator has measure zero on the sphere. On the other side, probability zero means that it is impossible, which it clearly isn't. What is the usual solution to this?

Probability zero is not the same as impossible.

CB

Thank you, FernandoRevilla and CaptainBlack. That answers my question.