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?

Re: basic question about probabililty = zero

Quote:

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 $\displaystyle (S,\mathcal{P}(S),p)$ with $\displaystyle S=\{a,b\}$ and $\displaystyle p$ defined by $\displaystyle p(\{a\})=0, p(\{b\})=1$ .

Re: basic question about probabililty = zero

Quote:

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

Re: basic question about probabililty = zero

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