A tetrahedron with four equilateral triangular faces has a sphere inscribed within it and a sphere circumscribed about it. For each of the four faces, there is a sphere tangent externally to the face at its center and to the circumscribed sphere. A point p is selected at random inside the circumscribed sphere. The probability that p lies inside one of the five shperes is closest to

a) 0 b) 0.1 c) 0.2 d) 0.3 e) 0.4

The answer is c.

And I am clueless how i could get any numbers at all.

Could someone take a look at my attached horrible drawing?

I just want to make sure I have the correct idea.

Vicky.