Spinning spherical target

May 2019
50
1
Mumbai (Bombay),Maharashtra State,India
Hello,

Three marksman simultaneously shoot and hit a rapidly spinning spherical target. What is the probability that the three points of impact lie on the same hemisphere?

I have to choose the correct answer from the following multiple choices given by the author.

1)0.

2)1.

3)$\frac12.$

4)$\frac23.$

5)$\frac14.$

6)$\frac18.$

What would be your answer?

My attempt:- How to answer this question? I think considering a great circle will be of much help here.
 

romsek

MHF Helper
Nov 2013
6,725
3,030
California
Think about this problem without any math for a bit. You'll have to consider an arrow hitting on the boundary of a hemisphere as being in the hemisphere.
 
Last edited:
May 2019
50
1
Mumbai (Bombay),Maharashtra State,India
Think about this problem without any math for a bit. You'll have to consider an arrow hitting on the boundary of a hemisphere as being in the hemisphere.
Hello,

So, what is your answer? and why? Please provide explanation so that i shall follow it correctly.
 

romsek

MHF Helper
Nov 2013
6,725
3,030
California
The answer is 1. Any three points on the sphere will lie in the same hemisphere.

I'm assuming that they mean any hemisphere. Not just the two defined by a great circle normal to the axis of rotation.
 
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