Difference between revisions of "2024 AMC 8 Problems/Problem 6"
(→Solution 1) |
(→Solution 1) |
||
| Line 7: | Line 7: | ||
==Solution 1== | ==Solution 1== | ||
| − | 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. | + | The answer is <math>D</math>. 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 | -Multpi12 | ||
Revision as of 12:39, 21 January 2024
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
