# basic question about probabililty = zero

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• Jul 9th 2011, 12:16 AM
nomadreid
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?
• Jul 9th 2011, 12:57 AM
FernandoRevilla
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 $(S,\mathcal{P}(S),p)$ with $S=\{a,b\}$ and $p$ defined by $p(\{a\})=0, p(\{b\})=1$ .
• Jul 9th 2011, 12:58 AM
CaptainBlack
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
• Jul 9th 2011, 11:17 PM
nomadreid
Re: basic question about probabililty = zero
Thank you, FernandoRevilla and CaptainBlack. That answers my question.