# 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.