2024 AMC 8 Problems/Problem 6

Problem

4 random points are chosen on a sphere. What is the probability that the tetrahedron with vertices of the 4 points contains the center of the sphere?

(A) 1/2 (B) 1/4 (C) 3/8 (D) 1/8 (E) 3/10 (Source: Putnam) lmao

Solution 1

The answer is . The are 8 possible rotations of the tetrahedron, using the Probability of Center Inclusion. Only one of these orientations could use the sphere, so it is 1/8.

-Multpi12