Three bullets are shot in a sphere. What is the probabilty that all of them end up in the same hemisphere? [closed]

Any ideas on how to solve it?

EDIT

The hemisphere is not predefined. It can be any hemisphere.

closed as unclear what you're asking by Did, John B, colormegone, Chill2Macht, LeucippusJun 13 '16 at 0:01

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• Is the hemisphere chosen ahead of time? – Semiclassical Jun 6 '16 at 17:36
• It depends a bit what you do between the different shots. Typically in interviews, you are supposed to check with the interviewer and ask him/her to clarify. If you don't move the gun between the shots then I would guess the probability is 100%. – Fabian Jun 6 '16 at 17:37
• I have edited the question @Semiclassical – user2331 Jun 6 '16 at 17:38
• Thanks. I'm not sure I'm visualizing it right, but if the hemisphere isn't chosen ahead of time (i.e. 'what is the probability that all three end up in 'some hemisphere') then I can hardly see how it wouldn't always be true. – Semiclassical Jun 6 '16 at 17:39
• There is a difference between saying "Three bullets are shot in a sphere" and "Three bullets are shot into a sphere". – DanielV Jun 7 '16 at 8:17

1 because three points define a plane (P) that does not in general contain the origin (we set apart the cases where this plane contains the origin $0$, which is of probability 0). Then it suffices to consider the plane parallel to (P) passing through the origin : it divides the sphere into two hemispheres, one of which contains the three points.