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Difference between revisions of "2024 AMC 8 Problems/Problem 6"

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==Problem==
 
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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?
 
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(A) 1/2 (B) 1/4 (C) 3/8 (D) 1/8 (E) 3/10
 
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(Source: Putnam)
 
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lmao
 
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==Solution 1==
 
==Solution 1==
 
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.   
 
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 13:01, 23 January 2024

Solution 1

The answer is $D$. 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
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