astronomy - What percentage of the sky is occluded by stars?

If you drew rays from the center of the earth out to infinity at every angle, what percentage of them would intersect a star?

Extra details:

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  Assume the rays are mathematical rays, or that they travel at infinite speeds.

  
  


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  Even in an infinite universe, since the apparent magnitude of stars decreases with distance, it is conceivable that the area occluded is less than 1, i.e. that the total magnitude of the stars at a given distance approaches zero as the distance increases.

  
  


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  Assume a snapshot of the universe as it currently exists.