Background

Constructing a simplified version of a problem is often one of the shortcuts to solving it

Problems

1. Randomly select three non-overlapping points on the circumference of a circle, connect the three points into a triangle, and find the probability that the center of the circle is within the triangle (also counted on the boundary)

{{ select(1) }}

• $\frac{1}{2}$
• $\frac{1}{4}$
• $\frac{1}{6}$
• $\frac{1}{8}$

2. Randomly select four non-overlapping points on the surface of a ball, connect the four points into a tetrahedron, and find the probability that the center of the sphere is within the tetrahedron (also calculated on the surface)

{{ select(2) }}

• $\frac{1}{2}$
• $\frac{1}{4}$
• $\frac{1}{6}$
• $\frac{1}{8}$