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Given a circle $C$ of radius $a$, a point is selected at random within the circle, what is the probability that the point is the centre of the circle?

Tom Lynd
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1 Answers1

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I assume that we're working in a real circle. Then the circle contains uncountably many points and so the probability is $0$, surely.

Stijn Hanson
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  • Thats what I thought but it seems unlikely. If the probability is $0$ then the event can never happen.. – Tom Lynd May 19 '14 at 10:12
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    No, probability $0$ doesn't mean that the event can't happen, that's only true in a finite state space. It's a similar problem to "Pick a real number". Any real number has probability $0$ of being chosen but some real number will be chosen. – Stijn Hanson May 19 '14 at 10:13
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    @TomLynd Have a look at this: http://math.stackexchange.com/questions/41107/zero-probability-and-impossibility – Jean-Claude Arbaut May 19 '14 at 10:13
  • That makes sense – Tom Lynd May 19 '14 at 10:23